Functional analysis and transforms Books
World Scientific Europe Ltd Modern Mathematical Methods For Scientists And
Book SynopsisModern Mathematical Methods for Scientists and Engineers is a modern introduction to basic topics in mathematics at the undergraduate level, with emphasis on explanations and applications to real-life problems. There is also an 'Application' section at the end of each chapter, with topics drawn from a variety of areas, including neural networks, fluid dynamics, and the behavior of 'put' and 'call' options in financial markets. The book presents several modern important and computationally efficient topics, including feedforward neural networks, wavelets, generalized functions, stochastic optimization methods, and numerical methods.A unique and novel feature of the book is the introduction of a recently developed method for solving partial differential equations (PDEs), called the unified transform. PDEs are the mathematical cornerstone for describing an astonishingly wide range of phenomena, from quantum mechanics to ocean waves, to the diffusion of heat in matter and the behavior of financial markets. Despite the efforts of many famous mathematicians, physicists and engineers, the solution of partial differential equations remains a challenge.The unified transform greatly facilitates this task. For example, two and a half centuries after Jean d'Alembert formulated the wave equation and presented a solution for solving a simple problem for this equation, the unified transform derives in a simple manner a generalization of the d'Alembert solution, valid for general boundary value problems. Moreover, two centuries after Joseph Fourier introduced the classical tool of the Fourier series for solving the heat equation, the unified transform constructs a new solution to this ubiquitous PDE, with important analytical and numerical advantages in comparison to the classical solutions. The authors present the unified transform pedagogically, building all the necessary background, including functions of real and of complex variables and the Fourier transform, illustrating the method with numerous examples.Broad in scope, but pedagogical in style and content, the book is an introduction to powerful mathematical concepts and modern tools for students in science and engineering.
£81.00
Imperial College Press Pseudo Differential Operators And Markov
Book SynopsisAfter recalling essentials of analysis — including functional analysis, convexity, distribution theory and interpolation theory — this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students.Trade Review"The book is carefully written and each chapter is concluded with interesting historical, contemporary, and bibliographical comments with indications for further reading." Mathematical Reviews, 2003Table of ContentsEssentials from analysis: calculus results; convexity; some interpolation theory. Fourier analysis and convolution semigroups: the Paley-Wiener-Schwartz theorem; bounded Borel measures and positive definite functions; convolution semigroups and negative definite functions; the Levy-Khinchin formula for continuous negative definite functions; Bernstein functions and subordination of convolution semigroups; Fourier multiplier theorems. One parameter semigroups: strongly continuous operator semigroups; subordination in the sense of Bochner for operator semigroups; generators of Feller semigroups; Dirichlet forms and generators of sub-Markovian semigroups; and other papers.
£148.50
Imperial College Press Pseudo Differential Operators And Markov
Book SynopsisIn this volume two topics are discussed: the construction of Feller and Lp-sub-Markovian semigroups by starting with a pseudo-differential operator, and the potential theory of these semigroups and their generators. The first part of the text essentially discusses the analysis of pseudo-differential operators with negative definite symbols and develops a symbolic calculus; in addition, it deals with special approaches, such as subordination in the sense of Bochner. The second part handles capacities, function spaces associated with continuous negative definite functions, Lp -sub-Markovian semigroups in their associated Bessel potential spaces, Stein's Littlewood-Paley theory, global properties of Lp-sub-Markovian semigroups, and estimates for transition functions.Trade Review"... this book is clearly written; theorems and propositions are well formulated and, if not proved, very adequate references are given." Mathematical Reviews, 2003Table of ContentsGenerators of Feller and sub-Markovian semigroups: second order elliptic differential operators; some second order hypoelliptic differential operators; pseudo-differential operators with negative definite symbols; Hoh's symbolic calculus; estimates for operators; constructing Feller and sub-Markovian semigroups; further analytic approaches; perturbation results; subordinate semigroups; operators of variable order of differentiation. Potential theory: capacities; abstract Bessel potential spaces; function spaces associated with continuous negative definite functions; sub-Markovian semigroups in their Bessel potential spaces; Stein's Littlewood-Paley theory; invariant sets, recurrence and transience; kernel representations and estimates for kernels; Nash-type inequalities and their consequences.
£135.00
New Academic Science Ltd Functional Analysis
Book Synopsis
£28.50
Springer Nature Switzerland AG Convex Functions and Their Applications: A
Book SynopsisThorough introduction to an important area of mathematics Contains recent results Includes many exercisesTable of ContentsConvex Functions on Intervals.- Convex Sets in Real Linear Spaces.- Convex Functions on a Normed Linear Space.- Convexity and Majorization.- Convexity in Spaces of Matrices.- Duality and Convex Optimization.- Special Topics in Majorization Theory.- A. Generalized Convexity on Intervals.- B. Background on Convex Sets.- C. Elementary Symmetric Functions.- D. Second Order Differentiability of Convex Functions.- E. The Variational Approach of PDE.
£42.74
Springer Nature Switzerland AG Geometric Singular Perturbation Theory Beyond the Standard Form
Book SynopsisThis volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.Table of ContentsIntroduction.- Motivating examples.- A coordinate-independent setup for GSPT.- Loss of normal hyperbolicity.- Relaxation oscillations in the general setting.- Pseudo singularities & canards.- What we did not discuss.
£52.24
Springer Nature Switzerland AG Spectral Theory: Basic Concepts and Applications
Book SynopsisThis textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature. Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrödinger operators, operators on graphs, and the spectral theory of Riemannian manifolds. Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course.Trade Review“The student will benefit from the many illustrative examples worked out in the book. … The author succeeds, and the hope is that after working on some of the examples presented, the student will want to explore further applications. Additionally, the instructor may also find inspiration for individual study topics that don’t require extensive prerequisites.” (Valentin Keyantuo, Mathematical Reviews, February, 2023)“This is an excellent textbook, which shall be a very useful tool for anyone who is oriented to the applications of functional analysis, especially to partial differential equations.” (Panagiotis Koumantos, zbMATH 1444.47001, 2020)Table of Contents1. Introduction.- 2. Hilbert Spaces.- 3. Operators.- 4. Spectrum and Resolvent.- 5. The Spectral Theorem.- 6. The Laplacian with Boundary Conditions.- 7. Schrödinger Operators.- 8. Operators on Graphs.- 9. Spectral Theory on Manifolds.- A. Background Material.- References.- Index.
£49.49
Springer Nature Switzerland AG Geometric Aspects of Functional Analysis: Israel
Book SynopsisContinuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn–Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed. Table of Contents- Jean Bourgain: In Memoriam. - A Generalized Central Limit Conjecture for Convex Bodies. - The Lower Bound for Koldobsky’s Slicing Inequality via Random Rounding. - Two-Sided Estimates for Order Statistics of Log-Concave Random Vectors. - Further Investigations of Rényi Entropy Power Inequalities and an Entropic Characterization of s-Concave Densities. - Small Ball Probability for the Condition Number of Random Matrices. - Concentration of the Intrinsic Volumes of a Convex Body. - Two Remarks on Generalized Entropy Power Inequalities. - On the Geometry of Random Polytopes. - Reciprocals and Flowers in Convexity. - Moments of the Distance Between Independent Random Vectors. - The Alon–Milman Theorem for Non-symmetric Bodies. - An Interpolation Proof of Ehrhard’s Inequality. - Bounds on Dimension Reduction in the Nuclear Norm. - High-Dimensional Convex Sets Arising in Algebraic Geometry. - Polylog Dimensional Subspaces of lN/∞. - On a Formula for the Volume of Polytopes.
£49.49
Springer Nature Switzerland AG Tools and Problems in Partial Differential Equations
Book SynopsisThis textbook offers a unique learning-by-doing introduction to the modern theory of partial differential equations.Through 65 fully solved problems, the book offers readers a fast but in-depth introduction to the field, covering advanced topics in microlocal analysis, including pseudo- and para-differential calculus, and the key classical equations, such as the Laplace, Schrödinger or Navier-Stokes equations. Essentially self-contained, the book begins with problems on the necessary tools from functional analysis, distributions, and the theory of functional spaces, and in each chapter the problems are preceded by a summary of the relevant results of the theory.Informed by the authors' extensive research experience and years of teaching, this book is for graduate students and researchers who wish to gain real working knowledge of the subject. Trade Review“Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in partial differential equations may find this work useful as a summary of analytic theories published in this volume.” (Vicenţiu D. Rădulescu, zbMATH 1461.35001, 2021)Table of ContentsPart I Tools and Problems.- 1 Elements of functional analysis and distributions.- 2 Statements of the problems of Chapter 1.- 3 Functional spaces.- 4 Statements of the problems of Chapter 3.- 5 Microlocal analysis.- 6 Statements of the problems of Chapter 5.- 7 The classical equations.- 8 Statements of the problems of Chapter 7.- Part II Solutions of the Problems. A Classical results. Index.
£41.24
Springer Nature Switzerland AG Complex Semisimple Quantum Groups and
Book SynopsisThis book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is comprehensive, beginning with background information on Hopf algebras, and ending with the classification of admissible representations of the q-deformation of a complex semisimple Lie group. The main components are: - a thorough introduction to quantized universal enveloping algebras over general base fields and generic deformation parameters, including finite dimensional representation theory, the Poincaré-Birkhoff-Witt Theorem, the locally finite part, and the Harish-Chandra homomorphism, - the analytic theory of quantized complex semisimple Lie groups in terms of quantized algebras of functions and their duals, - algebraic representation theory in terms of category O, and - analytic representation theory of quantized complex semisimple groups. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups.Trade Review“The book is largely self-contained. … It is highly recommended for mathematicians of all levels wishing to learn about these topics, in the algebraic setting and/or in the analytic setting.” (Huafeng Zhang, zbMATH 1514.20006, 2023)Table of Contents- Introduction. - Multiplier Hopf Algebras. - Quantized Universal Enveloping Algebras. - Complex Semisimple Quantum Groups. - Category O. - Representation Theory of Complex Semisimple Quantum Groups.
£47.49
Springer Nature Switzerland AG Explorations in Complex Functions
Book SynopsisThis textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book. Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into L-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener–Hopf method. Showcasing an array of accessible excursions, Explorations in Complex Functions is an ideal companion for graduate students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing a second course in complex analysis that builds on a first course prerequisite; exercises complement the results throughout.Trade Review“This is a suitable book with a proper concept at the right time. It is suitable because it shows the beauty, power and profundity of complex analysis, enlightens how many sided it is with all its inspirations and cross-connections to other branches of mathematics.” (Heinrich Begehr, zbMATH 1460.30001, 2021)Table of ContentsBasics.- Linear Fractional Transformations.- Hyperbolic geometry.- Harmonic Functions.- Conformal maps and the Riemann mapping theorem.- The Schwarzian derivative.- Riemann surfaces and algebraic curves.- Entire functions.- Value distribution theory.- The gamma and beta functions.- The Riemann zeta function.- L-functions and primes.- The Riemann hypothesis.- Elliptic functions and theta functions.- Jacobi elliptic functions.- Weierstrass elliptic functions.- Automorphic functions and Picard's theorem.- Integral transforms.- Theorems of Phragmén–Lindelöf and Paley–Wiener.- Theorems of Wiener and Lévy; the Wiener–Hopf method.- Tauberian theorems.- Asymptotics and the method of steepest descent.- Complex interpolation and the Riesz–Thorin theorem.
£49.49
Springer Nature Switzerland AG Finite Elements II: Galerkin Approximation,
Book SynopsisThis book is the second volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy.Volume II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.Table of ContentsPart V: Weak formulations and well-posedness.- Weak formulation of model problems.- Main results on well-posedness.- Part VI: Galerkin approximation.- Basic error analysis.- Error analysis with variational crimes.- Linear algebra.- Sparse matrices.- Quadratures.- Part VII: Elliptic PDEs: conforming approximation.- Scalar second-order elliptic PDEs.- H1-conforming approximation (I).- H1-conforming approximation (II).- A posteriori error analysis.- The Helmholtz problem.- Part VIII: Elliptic PDEs: nonconforming approximation.- Crouzeix-Raviart approximation.- Nitsche's boundary penalty method.- Discontinuous Galerkin.- Hybrid high-order methods.- Contrasted diffusivity (I).- Contrasted diffusivity (II).- Part IX: Vector-valued elliptic PDEs.- Linear elasticity.- Maxwell's equations: H(curl)-approximation.- Maxwell's equations: control on the divergence.- Maxwell's equations: further topics.- Part X: Eigenvalue problems.- Symmetric elliptic eigenvalue problems.- Symmetric operators, conforming approximation.- Nonsymmetric problems.- Part XI: PDEs in mixed form.- Well-posedness for PDEs in mixed form.- Mixed finite element approximation.- Darcy's equations.- Potential and flux recovery.- Stokes equations: Basic ideas.- Stokes equations: Stable Pairs (I).- Stokes equations: Stable pairs (II).- Appendices.- Bijective operators in Banach spaces.
£40.49
Springer Nature Switzerland AG The Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics: A Primer for Advanced Undergraduates
Book SynopsisThe field of elliptic functions, apart from its own mathematical beauty, has many applications in physics in a variety of topics, such as string theory or integrable systems. This book, which focuses on the Weierstrass theory of elliptic functions, aims at senior undergraduate and junior graduate students in physics or applied mathematics. Supplemented by problems and solutions, it provides a fast, but thorough introduction to the mathematical theory and presents some important applications in classical and quantum mechanics. Elementary applications, such as the simple pendulum, help the readers develop physical intuition on the behavior of the Weierstrass elliptic and related functions, whereas more Interesting and advanced examples, like the n=1 Lamé problem-a periodic potential with an exactly solvable band structure, are also presented.Table of ContentsWeierstrass Elliptic Function.- Weierstrass Quasi-periodic Functions.- Real Solutions of Weierstrass Equation.- Applications in Classical Mechanics.- Applications in Quantum Mechanics.- Epilogue and Projects for the Advanced Reader.
£52.24
Springer Nature Switzerland AG Point Process Calculus in Time and Space: An
Book SynopsisThis book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the study of stochastic models involving point processes, providing enough of the general theory for the reader to reach a technical level sufficient for most applications. Classical and not-so-classical models are examined in detail, including Poisson–Cox, renewal, cluster and branching (Kerstan–Hawkes) point processes.The applications covered in this text (queueing, information theory, stochastic geometry and signal analysis) have been chosen not only for their intrinsic interest but also because they illustrate the theory. Written in a rigorous but not overly abstract style, the book will be accessible to earnest beginners with a basic training in probability but will also interest upper graduate students and experienced researchers.Table of ContentsIntroduction.- Generalities.- Poisson Process on the Line.- Spatial Poisson Processes.- Renewal and Regenerative Processes.- Point Processes with a Stochastic Intensity.- Exvisible Intensity of Finite Point Processes.- Palm Probability on the Line.- Palm Probability in Space.- The Power Spectral Measure.- Information Content of Point Processes.- Point Processes in Queueing.- Hawkes Point Processes.- Appendices.- Bibliography.- Index.
£104.49
Springer Nature Switzerland AG Excursions in Harmonic Analysis, Volume 6: In
Book SynopsisJohn J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. The chapters in this volume – compiled on the occasion of his 80th birthday – are written by leading researchers in the field and pay tribute to John’s many significant and lasting achievements. Covering a wide range of topics in harmonic analysis and related areas, these chapters are organized into four main parts: harmonic analysis, wavelets and frames, sampling and signal processing, and compressed sensing and optimization. An introductory chapter also provides a brief overview of John’s life and mathematical career. This volume will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.Table of ContentsJohn Benedetto's mathematical work.- Absolute continuity and the Banach-Zaretsky Theorem.- Spectral Synthesis and H1(R).- Universal Upper Bound on the Blowup Rate of Nonlinear Schrodinger Equation with Rotation.- Almost Eigenvalues and Eigenvectors of Almost Mathieu Operators.- Spatio-spectral limiting on rendundant cubes: A case study.- A notion of optimal packings of subspaces with mix-rank and solutions.- Construction of Frames Using Calderon-Zygmund Operator Theory.- Equiangular frames and their duals.- Wavelet sets for crystallographic groups.- Discrete Translates in Function Spaces.- Local-to-global frames and applications to the dynamical sampling problem.- Signal analysis using Born-Jordan-type Distributions.- Sampling by averages and average splines on Dirichlet spaces and on combinatorial graphs.- Dynamical Sampling: a view from Control Theory.- Linear Multiscale Transforms Based on Even-Reversible Subdivision Operators.- Sparsity-Based MIMO Radars.- Robust width: A Characterization of uniformly stable and robust compressed sensing.- On best uniform affine approximants of convex or concave real valued functions from RK, Chebyshev equioscillation and graphics.- A Kaczmarz Algorithm for Solving Tree Based Distributed Systems of Equations.- Maximal function pooling with applications.
£104.49
Springer Nature Switzerland AG Geometric Aspects of Harmonic Analysis
Book SynopsisThis volume originated in talks given in Cortona at the conference "Geometric aspects of harmonic analysis" held in honor of the 70th birthday of Fulvio Ricci. It presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest mathematicians working in these areas. The subjects dealt with are topics of current interest in closely interrelated areas of Fourier analysis, singular integral operators, oscillatory integral operators, partial differential equations, multilinear harmonic analysis, and several complex variables.The work is addressed to researchers in the field.Table of Contents- An Extension Problem and Hardy Type Inequalities for the Grushin Operator. - Sharp Local Smoothing Estimates for Fourier Integral Operators. - On the Hardy–Littlewood Maximal Functions in High Dimensions: Continuous and Discrete Perspective. - Potential Spaces on Lie Groups. - On Fourier Restriction for Finite-Type Perturbations of the Hyperbolic Paraboloid. - On Young’s Convolution Inequality for Heisenberg Groups. - Young’s Inequality Sharpened. - Strongly Singular Integrals on Stratified Groups. - Singular Brascamp–Lieb: A Survey. - On the Restriction of Laplace–Beltrami Eigenfunctions and Cantor-Type Sets. - Basis Properties of the Haar System in Limiting Besov Spaces. - Obstacle Problems Generated by the Estimates of Square Function. - Of Commutators and Jacobians. - On Regularity and Irregularity of Certain Holomorphic Singular Integral Operators.
£151.99
Springer Nature Switzerland AG Advances in Matrix Inequalities
Book SynopsisThis self-contained monograph unifies theorems, applications and problem solving techniques of matrix inequalities. In addition to the frequent use of methods from Functional Analysis, Operator Theory, Global Analysis, Linear Algebra, Approximations Theory, Difference and Functional Equations and more, the reader will also appreciate techniques of classical analysis and algebraic arguments, as well as combinatorial methods. Subjects such as operator Young inequalities, operator inequalities for positive linear maps, operator inequalities involving operator monotone functions, norm inequalities, inequalities for sector matrices are investigated thoroughly throughout this book which provides an account of a broad collection of classic and recent developments. Detailed proofs for all the main theorems and relevant technical lemmas are presented, therefore interested graduate and advanced undergraduate students will find the book particularly accessible. In addition to several areas of theoretical mathematics, Matrix Analysis is applicable to a broad spectrum of disciplines including operations research, mathematical physics, statistics, economics, and engineering disciplines. It is hoped that graduate students as well as researchers in mathematics, engineering, physics, economics and other interdisciplinary areas will find the combination of current and classical results and operator inequalities presented within this monograph particularly useful.Trade Review“The book is written in a readable style and provides several interesting and nice techniques. It is very useful for graduate students and researchers interested in operator and norm inequalities.” (Mohammad Sal Moslehian, Mathematical Reviews, June, 2023)The book contains a bibliography of over 200 items and … the many inequalities presented, usually with full proofs provided. … if you are looking for an inequality in the areas covered, then this should be a useful source.” (John D. Dixon, zbMATH 1477.15001, 2022)Table of Contents1. Elementary linear algebra review.- 2. Interpolating the arithmetic-geometric mean inequality and its operator version.- 3. Operator inequalities for positive linear maps.- 4. Operator inequalities involving operator monotone functions.- 5. Inequalities for sector matrices.- 6. Positive partial transpose matrix inequalities.- References.- Index.
£98.99
Springer Nature Switzerland AG Differentiability in Banach Spaces, Differential
Book SynopsisThis book is divided into two parts, the first one to study the theory of differentiable functions between Banach spaces and the second to study the differential form formalism and to address the Stokes' Theorem and its applications. Related to the first part, there is an introduction to the content of Linear Bounded Operators in Banach Spaces with classic examples of compact and Fredholm operators, this aiming to define the derivative of Fréchet and to give examples in Variational Calculus and to extend the results to Fredholm maps. The Inverse Function Theorem is explained in full details to help the reader to understand the proof details and its motivations. The inverse function theorem and applications make up this first part. The text contains an elementary approach to Vector Fields and Flows, including the Frobenius Theorem. The Differential Forms are introduced and applied to obtain the Stokes Theorem and to define De Rham cohomology groups. As an application, the final chapter contains an introduction to the Harmonic Functions and a geometric approach to Maxwell's equations of electromagnetism.Trade Review“A specific feature of the book is the abundance of examples from mechanics, physics, calculus of variations, illustrating the abstract concepts introduced in the main text. … There are a lot of exercises spread through the book, some elementary, while others are more advanced. The book can be used as supplementary material for undergraduate or graduate level courses, as well as by the students in physics interested in a mathematical treatment of some important problems in their domain.” (Stefan Cobzaş, zbMATH 1479.46001, 2022)Table of ContentsIntroduction.- Chapter 1. Differentiation in R^n.- Chapter 2. Linear Operators in Banach Spaces.- Chapter 3. Differentiation in Banach Spaces.- Chapter 4. Vector Fields.- Chapter 5. Vectors Integration, Potential Theory.- Chapter 6. Differential Forms, Stoke’s Theorem.- Chapter 7. Applications to the Stoke’s Theorem.- Appendix A. Basics of Analysis.- Appendix B. Differentiable Manifolds, Lie Groups.- Appendix C. Tensor Algebra.- Bibliography.- Index.
£52.24
Springer Nature Switzerland AG Zero Product Determined Algebras
Book SynopsisThis book provides a concise survey of the theory of zero product-determined algebras, which has been developed over the last 15 years. It is divided into three parts. The first part presents the purely algebraic branch of the theory, the second part presents the functional analytic branch, and the third part discusses various applications. The book is intended for researchers and graduate students in ring theory, Banach algebra theory, and nonassociative algebra.Trade Review“This book is about zero product determined algebras and is written in an attractive way. It deals with the introduction and study of this class of algebras. Most of this book is taken from research articles from the last 15 years and is suitable for researchers in this field and students with different backgrounds and can be used for self-study.” (Hoger Ghahramani, Mathematical Reviews, March, 2023)Table of Contents- Part I Algebraic Theory. - Zero Product Determined Nonassociative Algebras. - Zero Product Determined Rings and Algebras. - Zero Lie/Jordan Product Determined Algebras. - Part II Analytic Theory. - Zero Product Determined Nonassociative Banach Algebras. - Zero Product Determined Banach Algebras. - Zero Lie/Jordan Product Determined Banach Algebras. - Part III Applications. - Homomorphisms and Related Maps. - Derivations and Related Maps. - Miscellany.
£44.99
Springer Nature Switzerland AG Harmonic Analysis on the Real Line: A Path in the
Book SynopsisThis book sketches a path for newcomers into the theory of harmonic analysis on the real line. It presents a collection of both basic, well-known and some less known results that may serve as a background for future research around this topic. Many of these results are also a necessary basis for multivariate extensions. An extensive bibliography, as well as hints to open problems are included. The book can be used as a skeleton for designing certain special courses, but it is also suitable for self-study.Trade Review“The book under review takes the reader on a journey along a particular path through the vast landscape of modern harmonic analysis in one real variable. From beginning to end, the text is uniquely flavored by the author’s mathematical interests which provides the reader with a good sense of direction. … The book should be accessible to beginning graduate students in analysis and advanced undergraduates with basic knowledge in real analysis … .” (Joris Roos, zbMATH 1514.42001, 2023)“This book is very accurately described by its subtitle ‘a path in the theory’. The book is at times a textbook, an introduction to harmonic analysis, an essay, or a survey, or some combination of these. … Some theorems are stated and proved, some are discussed, and others are quickly mentioned. It's not a standard path, but an engaging one, offering insights and connections that are new or not well known.” (Charles N. Moore, Mathematical Reviews, September, 2022)Table of Contents- Introduction. - Classes of Functions. - Fourier Series. - Fourier Transform. - Hilbert Transform. - Hardy Spaces and their Subspaces. - Hardy Inequalities. - Certain Applications.
£49.49
Springer Nature Switzerland AG Upper and Lower Bounds for Stochastic Processes:
Book SynopsisThis book provides an in-depth account of modern methods used to bound the supremum of stochastic processes. Starting from first principles, it takes the reader to the frontier of current research. This second edition has been completely rewritten, offering substantial improvements to the exposition and simplified proofs, as well as new results.The book starts with a thorough account of the generic chaining, a remarkably simple and powerful method to bound a stochastic process that should belong to every probabilist’s toolkit. The effectiveness of the scheme is demonstrated by the characterization of sample boundedness of Gaussian processes. Much of the book is devoted to exploring the wealth of ideas and results generated by thirty years of efforts to extend this result to more general classes of processes, culminating in the recent solution of several key conjectures.A large part of this unique book is devoted to the author’s influential work. While many of the results presented are rather advanced, others bear on the very foundations of probability theory. In addition to providing an invaluable reference for researchers, the book should therefore also be of interest to a wide range of readers.Trade Review“The book includes a rich collection of exercises that will allow the reader to gain skills for a better understanding. The book is then suitable as a textbook for an advanced course. … The systematic and deep treatment of the subject under study makes the book a good reference for the specialist.” (Erick Treviño-Aguilar, Mathematical Reviews, March, 2023)Table of Contents1. What is This Book About? Part I The Generic Chaining.- 2 Gaussian Processes and the Generic Chaining.- 3 Trees and Other Measures of Size.- 4 Matching Theorems.- Part II Some Dreams Come True.- 5 Warming Up with p-Stable Processes.- 6 Bernoulli Processes.- 7 Random Fourier Series and Trigonometric Sums.- 8 Partitioning Scheme and Families of Distances.- 9 Peaky Part of Functions.- 10 Proof of the Bernoulli Conjecture.- 11 Random Series of Functions.- 12 Infinitely Divisible Processes.- 13 Unfulfilled Dreams.- Part III Practicing.- 14 Empirical Processes, II.- 15 Gaussian Chaos.- 16 Convergence of Orthogonal Series; Majorizing Measures.- 17 Shor's Matching Theorem.- 18 The Ultimate Matching Theorem in Dimension Three.- 19 Application to Banach Space Theory.- A Discrepancy for Convex Sets.- B Some Deterministic Arguments.- C Classical View of Infinitely Divisible Processes.- D Reading Suggestions.- E Research Directions.- F Solutions of Selected Exercises.- G Comparison with the First Edition.- References.- Index.
£123.49
Springer Nature Switzerland AG Transcendence in Algebra, Combinatorics, Geometry
Book SynopsisThis proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.Table of ContentsFrobenius action on a hypergeometric curve and an algorithm for computing values of Dwork’s p-adic hypergeometric functions (Asakura).- A Matrix version of Dwork’s Congruences (Beukers).- On the kernel curves associated with walks in the quarter plane (Singer).- A survey on the hypertranscendence of the solutions of the Schröder's, Böttcher's and Abel's equations (Fernandes).- Hodge structures and differential operators (Vlasenko).- Beck-type identities for Euler pairs of order (Welch et al.).- Quarter-plane lattice paths with interacting boundaries: the Kreweras and reverse Kreweras models (Xu et al.).- Infinite product formulae for generating functions for sequences of squares (Radu et al.).- A theta identity of Gauss connecting functions from additive and multiplicative number theory (Merca).- Combinatorial quantum field theory and the Jacobian conjecture (Tanasa).- How regular are regular singularities? (Hauser).- Néron desingularization of extensions of valuation rings with an appendix by kęstutis česnavičius (Popescu).- Diagonal Representation of Algebraic Power Series: A Glimpse Behind the Scenes (Yurkevich).- Proof of chudnovskys’ hypergeometric series for 1/π using weber modular polynomials (Guillera).-Computing an order-complete basis for m∞(n) and applications (Radu et al.).- An algorithm to prove holonomic differential equations for modular forms (Radu et al.).- A case study for ζ(4) (zudilin et al.).- Support of an algebraic series as the range of a recursive sequence (bell).- X-coordinates of pell equations in various sequences (luca).- A conditional proof of the leopoldt conjecture for cm fields (mihailescu).- Siegel’s problem for e-functions of order 2 (Roques et al.).- Irrationality and Transcendence of Alternating Series Via Continued Fractions (Snowdow).- On the transcendence of critical hecke l-values (sprang).
£134.99
Springer Nature Switzerland AG A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
Book SynopsisIn 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic properties of the gamma function using elementary methods of the calculus. Bohr-Mollerup's theorem was then adopted by Nicolas Bourbaki as the starting point for his exposition of the gamma function.This open access book develops a far-reaching generalization of Bohr-Mollerup's theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generalization shows using elementary techniques that a very rich spectrum of functions satisfy analogues of several classical properties of the gamma function, including Bohr-Mollerup's theorem itself, Euler's reflection formula, Gauss' multiplication theorem, Stirling's formula, and Weierstrass' canonical factorization.The scope of the theory developed in this work is illustrated through various examples, ranging from the gamma function itself and its variants and generalizations (q-gamma, polygamma, multiple gamma functions) to important special functions such as the Hurwitz zeta function and the generalized Stieltjes constants. This volume is also an opportunity to honor the 100th anniversary of Bohr-Mollerup's theorem and to spark the interest of a large number of researchers in this beautiful theory.Table of ContentsPreface.- List of main symbols.- Table of contents.- Chapter 1. Introduction.- Chapter 2. Preliminaries.- Chapter 3. Uniqueness and existence results.- Chapter 4. Interpretations of the asymptotic conditions.- Chapter 5. Multiple log-gamma type functions.- Chapter 6. Asymptotic analysis.- Chapter 7. Derivatives of multiple log-gamma type functions.- Chapter 8. Further results.- Chapter 9. Summary of the main results.- Chapter 10. Applications to some standard special functions.- Chapter 11. Definining new log-gamma type functions.- Chapter 12. Further examples.- Chapter 13. Conclusion.- A. Higher order convexity properties.- B. On Krull-Webster's asymptotic condition.- C. On a question raised by Webster.- D. Asymptotic behaviors and bracketing.- E. Generalized Webster's inequality.- F. On the differentiability of \sigma_g.- Bibliography.- Analogues of properties of the gamma function.- Index.
£26.24
Springer Nature Switzerland AG Generalized B*-Algebras and Applications
Book SynopsisThis book reviews the theory of 'generalized B*-algebras' (GB*-algebras), a class of complete locally convex *-algebras which includes all C*-algebras and some of their extensions. A functional calculus and a spectral theory for GB*-algebras is presented, together with results such as Ogasawara's commutativity condition, Gelfand–Naimark type theorems, a Vidav–Palmer type theorem, an unbounded representation theory, and miscellaneous applications. Numerous contributions to the subject have been made since its initiation by G.R. Allan in 1967, including the notable early work of his student P.G. Dixon. Providing an exposition of existing research in the field, the book aims to make this growing theory as familiar as possible to postgraduate students interested in functional analysis, (unbounded) operator theory and its relationship to mathematical physics. It also addresses researchers interested in extensions of the celebrated theory of C*-algebras.Trade Review“This book deals with the theory of locally convex algebras, in general, and of generalized B_-algebras (GB_-algebras in short) in particular. It is well written and self-contained.” (Lahbib Oubbi, Mathematical Reviews, November, 2023)“The book has been written by specialists that are actively working in the field. The choice of the presented material has been done with great care. The bibliography contains all classical monographs, all important papers, and most recent ones. The book leads the reader 'smoothly' ... . It will therefore serve as an excellent introduction to this theory for graduate students. It should also provide a valuable reference source for researchers in the field.” (Andrzej Sołtysiak, zbMATH 1498.46001, 2022)Table of Contents1. Introduction.- 2. A Spectral Theory for Locally Convex Algebras.- 3. Generalized B*-Algebras: Functional Representation Theory.- 4. Commutative Generalized B*-Algebras: Functional Calculus and Equivalent Topologies.- 5. Extended C*-Algebras and Extended W*-Algebras.- 6. Generalized B*-Algebras: Unbounded *-Representation Theory.- 7. Applications I: Miscellanea.- 8. Applications II: Tensor Products.
£47.49
Springer International Publishing AG Wave Packet Analysis of Feynman Path Integrals
Book SynopsisThe purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators.In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets – can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction.This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.Table of Contents- Itinerary - How Gabor Analysis met Feynman Path Integrals. - Part I Elements of Gabor Analysis. - Basic Facts of Classical Analysis. - The Gabor Analysis of Functions. - The Gabor Analysis of Operators. - Semiclassical Gabor Analysis. - Part II Analysis of Feynman Path Integrals. - Pointwise Convergence of the Integral Kernels. - Convergence in L(L2) - Potentials in the Sjöstrand Class. - Convergence in L(L2) - Potentials in Kato-Sobolev Spaces. - Convergence in the Lp Setting.
£49.49
Springer International Publishing AG Analysis and Quantum Groups
Book SynopsisThis volume presents a completely self-contained introduction to the elaborate theory of locally compact quantum groups, bringing the reader to the frontiers of present-day research. The exposition includes a substantial amount of material on functional analysis and operator algebras, subjects which in themselves have become increasingly important with the advent of quantum information theory. In particular, the rather unfamiliar modular theory of weights plays a crucial role in the theory, due to the presence of ‘Haar integrals’ on locally compact quantum groups, and is thus treated quite extensively The topics covered are developed independently, and each can serve either as a separate course in its own right or as part of a broader course on locally compact quantum groups. The second part of the book covers crossed products of coactions, their relation to subfactors and other types of natural products such as cocycle bicrossed products, quantum doubles and doublecrossed products. Induced corepresentations, Galois objects and deformations of coactions by cocycles are also treated. Each section is followed by a generous supply of exercises. To complete the book, an appendix is provided on topology, measure theory and complex function theory.Table of ContentsPreface.- Set theoretic preliminaries.- Banach spaces.- Bases in Banach spaces.- Operators on Hilbert spaces.- Spectral theory.- States and representations.- Types of von Neumann algebras.- Tensor products.- Unbounded operators.- Tomita-Takesaki theory.- Spectra and type III factors.- Quantum groups and duality.- Special cases.- Classical crossed products.- Crossed products for quantum groups.- Generalized and continuous crossed products.- Basic construction and quantum groups.- Galois objects and cocycle deformations.- Doublecrossed products of quantum groups.- Induction.-Appendix.- Bibliography.- Index.- Exercises.
£80.99
Springer International Publishing AG Functional Analysis Tools for Practical Use in
Book SynopsisThis textbook describes selected topics in functional analysis as powerful tools of immediate use in many fields within applied mathematics, physics and engineering. It follows a very reader-friendly structure, with the presentation and the level of exposition especially tailored to those who need functional analysis but don’t have a strong background in this branch of mathematics. For every tool, this work emphasizes the motivation, the justification for the choices made, and the right way to employ the techniques. Proofs appear only when necessary for the safe use of the results. The book gently starts with a road map to guide reading. A subsequent chapter recalls definitions and notation for abstract spaces and some function spaces, while Chapter 3 enters dual spaces. Tools from Chapters 2 and 3 find use in Chapter 4, which introduces distributions. The Linear Functional Analysis basic triplet makes up Chapter 5, followed by Chapter 6, which introduces the concept of compactness. Chapter 7 brings a generalization of the concept of derivative for functions defined in normed spaces, while Chapter 8 discusses basic results about Hilbert spaces that are paramount to numerical approximations. The last chapter brings remarks to recent bibliographical items. Elementary examples included throughout the chapters foster understanding and self-study. By making key, complex topics more accessible, this book serves as a valuable resource for researchers, students, and practitioners alike that need to rely on solid functional analysis but don’t need to delve deep into the underlying theory.Table of ContentsRoad Map.- Basic Concepts.- Dual of a Normed Space.- Sobolev Spaces, Distributions.- The Three Basic Principles.- Compactness.- Function Derivatives in Normed Spaces.- Hilbert Bases and Approximations.
£40.49
Springer International Publishing AG Partial Differential Equations: An Introduction
Book SynopsisThis textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with Maple™ completes the book. Throughout, three fundamental examples are studied with different tools: Poisson’s equation, the heat equation, and the wave equation on Euclidean domains. The Black–Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.Table of Contents1 Modeling, or where do differential equations come from.- 2 Classification and characteristics.- 3 Elementary methods.- 4 Hilbert spaces.- 5 Sobolev spaces and boundary value problems in dimension one.- 6 Hilbert space methods for elliptic equations.- 7 Neumann and Robin boundary conditions.- 8 Spectral decomposition and evolution equations.- 9 Numerical methods.- 10 Maple®, or why computers can sometimes help.- Appendix.
£53.99
Springer International Publishing AG Fixed Point Theory in Generalized Metric Spaces
Book SynopsisThis book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.Table of ContentsMetric Spaces.- Extension of Metric Spaces.- Fixed Point Theorems on Extended Metric Spaces.
£44.99
Springer International Publishing AG More (Almost) Impossible Integrals, Sums, and
Book SynopsisThis book, the much-anticipated sequel to (Almost) Impossible, Integrals, Sums, and Series, presents a whole new collection of challenging problems and solutions that are not commonly found in classical textbooks. As in the author’s previous book, these fascinating mathematical problems are shown in new and engaging ways, and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Classical problems are shown in a fresh light, with new, surprising or unconventional ways of obtaining the desired results devised by the author. This book is accessible to readers with a good knowledge of calculus, from undergraduate students to researchers. It will appeal to all mathematical puzzlers who love a good integral or series and aren’t afraid of a challenge.Table of ContentsChapter 1. Integrals.- Chapter 2. Hints.- Chapter 3. Solutions.- Chapter 4. Sums and Series.- Chapter 5. Hints.- Chapter 6. Solutions.
£49.49
Springer International Publishing AG The E. M. Stein Lectures on Hardy Spaces
Book SynopsisThe book The E. M. Stein Lectures on Hardy Spaces is based on a graduate course on real variable Hardy spaces which was given by E.M. Stein at Princeton University in the academic year 1973-1974. Stein, along with C. Fefferman and G. Weiss, pioneered this subject area, removing the theory of Hardy spaces from its traditional dependence on complex variables, and to reveal its real-variable underpinnings.This book is based on Steven G. Krantz’s notes from the course given by Stein. The text builds on Fefferman's theorem that BMO is the dual of the Hardy space. Using maximal functions, singular integrals, and related ideas, Stein offers many new characterizations of the Hardy spaces. The result is a rich tapestry of ideas that develops the theory of singular integrals to a new level. The final chapter describes the major developments since 1974.This monograph is of broad interest to graduate students and researchers in mathematical analysis. Prerequisites for the book include a solid understanding of real variable theory and complex variable theory. A basic knowledge of functional analysis would also be useful.Table of ContentsIntroductory material.- More on Hardy Spaces.- Background on H^p Spaces.- Hardy Spaces on D.- Hardy Spaces on R^n.- Developments Since 1974.- Concluding Remarks.- Bibliography.- Index.
£49.49
Springer International Publishing AG An Introduction to Partial Differential Equations
Book SynopsisThis textbook is an introduction to the methods needed to solve partial differential equations (PDEs). Readers are introduced to PDEs that come from a variety of fields in engineering and the natural sciences. The chapters include the following topics: First Order PDEs, Second Order PDEs, Fourier Series, Separation of Variables, the Fourier Transform, and higher dimensional problems. Readers are guided through these chapters where techniques for solving first and second order PDEs are introduced. Each chapter ends with series of exercises to facilitate learning as well as illustrate the material presented in each chapter. Table of ContentsIntroduction.- First Order PDEs.- Second Order Linear PDEs.- Fourier Series.- Separation of Variables.- Fourier Transform.
£33.24
Springer International Publishing AG Functional Analysis
Book SynopsisThis textbook provides an introduction to functional analysis suitable for lecture courses to final year undergraduates or beginning graduates. Starting from the very basics of metric spaces, the book adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, including the spectral theorem, the Gelfand transform, and Banach algebras. Various applications, such as least squares approximation, inverse problems, and Tikhonov regularization, illustrate the theory. Over 1000 worked examples and exercises of varying difficulty present the reader with ample material for reflection. This new edition of Functional Analysishas been completely revised and corrected, withmany passages rewritten for clarity, numerous arguments simplified, and a good amount of new material added, including new examples and exercises. The prerequisites, however, remain the same with only knowledge of linear algebra and real analysis of a singlevariable assumed of the reader.
£44.99
Springer International Publishing AG CAlgebras and Mathematical Foundations of Quantum
Book Synopsis
£49.49
Springer International Publishing AG Fundamentals of Convex Analysis and Optimization:
Book SynopsisThis book aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It presents an original and systematic treatment of convex analysis, covering standard results and improved calculus rules in subdifferential analysis. The tools supplied in the text allow a direct approach to the mathematical foundations of convex optimization, in particular to optimality and duality theory. Other applications in the book concern convexification processes in optimization, non-convex integration of the Fenchel subdifferential, variational characterizations of convexity, and the study of Chebychev sets. At the same time, the underlying geometrical meaning of all the involved concepts and operations is highlighted and duly emphasized. A notable feature of the book is its unifying methodology, as well as the novelty of providing an alternative or complementary view to the traditional one in which the discipline is presented to students and researchers. This textbook can be used for courses on optimization, convex and variational analysis, addressed to graduate and post-graduate students of mathematics, and also students of economics and engineering. It is also oriented to provide specific background for courses on optimal control, data science, operations research, economics (game theory), etc. The book represents a challenging and motivating development for those experts in functional analysis, convex geometry, and any kind of researchers who may be interested in applications of their work.Table of Contents1. Introduction1.1 Motivation1.2 Historical antecedents1.3 Working framework and objectives2. Preliminaries2.1 Functional analysis background2.2 Convexity and continuity2.3 Examples of convex functions2.4 Exercises2.5 Bibliographical notes 3. Fenchel-Moreau-Rockafellar theory3.1 Conjugation theory3.2 Fenchel-Moreau-Rockafellar theorem3.3 Dual representations of support functions3.4 Minimax theory3.5 Exercises3.6 Bibliographical notes4. Fundamental topics in convex analysis4.1 Subdifferential theory4.2 Convex duality4.3 Convexity in Banach spaces4.4 Subdifferential integration4.5 Exercises4.6 Bibliographical notes5. Supremum of convex functions5.1 Conjugacy based approach5.2 Main subdifferential formulas 5.3 The role of continuity assumptions5.4 Exercises5.5 Bibliographical notes 6. The supremum in specific contexts6.1 The compact-continuous setting6.2 Compactification approach6.3 Main subdifferential formula revisited 6.4 Homogeneous formulas6.5 Qualification conditions 6.6 Exercises6.7 Bibliographical notes7. Other subdifferential calculus rules7.1 Subdifferential of the sum7.2 Symmetric versus asymmetric conditions7.3 Supremum-sum subdifferential calculus 7.4 Exercises7.5 Bibliographical notes8. Miscellaneous8.1 Convex systems and Farkas-type qualifications8.2 Optimality and duality in (semi)infinite convex optimization8.3 Convexification processes in optimization8.4 Non-convex integration8.5 Variational characterization of convexity8.6 Chebychev sets and convexity8.7 Exercises8.8 Bibliographical notes 9. Exercises- Solutions9.1 Exercises of chapter 29.2 Exercises of chapter 39.3 Exercises of chapter 49.4 Exercises of chapter 59.5 Exercises of chapter 69.6 Exercises of chapter 79.7 Exercises of chapter 8 IndexGlossary of NotationsBibliography
£49.49
Springer International Publishing AG Pseudo-Monotone Operator Theory for Unsteady
Book SynopsisThis book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(.,.)-Navier–Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(.,.) in this system, the classical weak existence analysis based on the pseudo-monotone operator theory in the framework of Bochner–Lebesgue spaces is not applicable. As a substitute for Bochner–Lebesgue spaces, variable Bochner–Lebesgue spaces are introduced and analyzed. In the mathematical framework of this substitute, the theory of pseudo-monotone operators is extended to unsteady problems with variable exponents, leading to the weak solvability of the unsteady p(.,.)-Navier–Stokes equations under general assumptions.Aimed primarily at graduate readers, the book develops the material step-by-step, starting with the basics of PDE theory and non-linear functional analysis. The concise introductions at the beginning of each chapter, together with illustrative examples, graphics, detailed derivations of all results and a short summary of the functional analytic prerequisites, will ease newcomers into the subject.Table of Contents- 1. Introduction. - 2. Preliminaries. - Part I Main Part. - 3. Variable Bochner–Lebesgue Spaces. - 4. Solenoidal Variable Bochner–Lebesgue Spaces. - 5. Existence Theory for Lipschitz Domains. - Part II Extensions. - 6. Pressure Reconstruction. - 7. Existence Theory for Irregular Domains. - 8. Existence Theory for p- < 2. - 9. Appendix.
£49.49
Springer International Publishing AG Fractional Differential Equations: New
Book SynopsisThis book covers problems involving a variety of fractional differential equations, as well as some involving the generalized Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations based on the most recent research in the area. The book discusses the classic and novel fixed point theorems related to the measure of noncompactness in Banach spaces and explains how to utilize them as tools. The authors build each chapter upon the previous one, helping readers to develop their understanding of the topic. The book includes illustrated results, analysis, and suggestions for further study.Table of ContentsIntroduction.- Preliminary Background.- Hybrid Fractional Differential Equations.- Fractional Differential Equations with Retardation and Anticipation.- Impulsive Fractional Differential Equations with Retardation and Anticipation.- Coupled Systems for Fractional Differential Equations.
£31.49
Springer International Publishing AG Representations of SU(2,1) in Fourier Term
Book SynopsisThis book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the “abelian” Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the “non-abelian” modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included.These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms.Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.Table of Contents- 1. Introduction. - 2. The Lie Group SU(2,1) and Subgroups. - 3. Fourier Term Modules. - 4. Submodule Structure. - 5. Application to Automorphic Forms.
£44.99
Birkhauser Verlag AG Noncommutative Integration and Operator Theory
Book SynopsisThe purpose of this monograph is to provide a systematic account of the theory of noncommutative integration in semi-finite von Neumann algebras. It is designed to serve as an introductory graduate level text as well as a basic reference for more established mathematicians with interests in the continually expanding areas of noncommutative analysis and probability. Its origins lie in two apparently distinct areas of mathematical analysis: the theory of operator ideals going back to von Neumann and Schatten and the general theory of rearrangement invariant Banach lattices of measurable functions which has its roots in many areas of classical analysis related to the well-known Lp-spaces. A principal aim, therefore, is to present a general theory which contains each of these motivating areas as special cases.Table of Contents- 1. A Review of Relevant Operator Theory. - 2. Measurable Operators. - 3. Singular Value Functions. - 4. Symmetric Spaces of τ-Measurable Operators. - 5. Strongly Symmetric Spaces of τ-Measurable Operators. - 6. Examples. - 7. Interpolation.
£125.99
Springer A Spectral Theory Of Noncommuting Operators
Book Synopsis1 Characteristic Polynomial in Several Variables.- 2 Finite Dimensional Group Representations.- 3 Finite Dimensional Lie Algebras.- 4 Projective Spectrum in Banach Algebras.- 5 The C?-algebra of the Infinite Dihedral Group.- 6 The Maurer-Cartan Form of Operator Pencils.- 7 Hermitian Metrics on the Resolvent Set.- 8 Compact Operators and Kernel Bundles.- 9 Weak Containment and Amenability.- 10 Self-similarity and Julia Sets.- References.
£59.99
Springer International Publishing AG Functional Analysis and Operator Theory
Book SynopsisThe book contains a collection of more than 800 problems from all main chapters of functional analysis, with theoretical background and solutions. It is mostly intended for undergraduate students who are starting to study the course of functional analysis. The book will also be useful for graduate and post- graduate students and researchers who wish to refresh their knowledge and deepen their understanding of the subject, as well as for teachers of functional analysis and related disciplines. It can be used for independent study as well. It is assumed that the reader has mastered standard courses of calculus and measure theory and has basic knowledge of linear algebra, analytic geometry, and differential equations. This collection of problems can help students of different levels of training and different areas of specialization to learn how to solve problems in functional analysis. Each chapter of the book has similar structure and consists of the following sections: Theoretical Background, Examples of Problems with Solutions, and Problems to Solve. The book contains theoretical preliminaries to ensure that the reader understands the statements of problems and is able to successfully solve them. Then examples of typical problems with detailed solutions are included, and this is relevant not only for those students who have significant difficulties in studying this subject, but also for other students who due to various circumstances ?could be deprived of communication with a teacher. There are problems for independent solving, and the corresponding selection of problems reflects all the main plot lines that relate to a given topic. The number of problems is sufficient both for a teacher to give practical lessons, to set homework, to prepare tasks for various forms of control, and for those students who want to study the discipline more deeply. Problems of a computational nature are provided with answers, while theoretical problems, the solutions ofwhich require non-trivial ideas or new techniques, are provided with detailed hints or solutions to introduce the reader to the corresponding ideas or techniques.
£62.99
Springer Upper Bounds for Grothendieck Constants Quantum
Book Synopsis- Introduction and motivation.- Complex Gaussian random vectors and their probability law.- A quantum correlation matrix version of the Grothendieck inequality.- Powers of inner products of random vectors, uniformly distributed on the sphere.- Completely correlation preserving functions.- The real case: towards extending Krivine's approach.- The complex case: towards extending Haagerup's approach.- A summary scheme of the main result.- Concluding remarks and open problems.- References.- Index.
£49.49
Birkhauser Verlag AG Advanced Techniques with Block Matrices of
Book SynopsisThis book introduces several powerful techniques and fundamental ideas involving block matrices of operators, as well as matrices with elements in a C*-algebra.
£44.99
Springer Principal Symbol Calculus on Contact Manifolds
Book SynopsisPreface.- Foreword by Nigel Higson.- Introduction.- Principal Symbol on the Heisenberg Group.- Equivariance of the Principal Symbol Under Heisenberg Diffeomorphisms.- Principal Symbol on Contact Manifolds.- Bibliography.
£49.49
Springer Approximate Fixed Points of Nonexpansive Mappings
Book SynopsisPreface.- 1. Introduction.- 2. Asymptotic regularity for iterations of nonexpansive mappings.- 3. Asymptotic regularity for iterations of monotone nonexpansive mappings.- 4. Asymptotic regularity of uniformly locally nonexpansive mappings.- 5. Asymptotic regularity property in spaces with graphs.- 6. Inexact Viscosity Approximation Methods in Hilbert Spaces.- 7. A common fixed point problem.- 8. Perov contraction mappings.- 9. Cyclical mappings.- 10. Monotone nonexpansive mappings.- 11. Uniformly Locally Contractive Mappings.- 12. Set-valued mappings.- 13. Nonexpansive mappings in spaces with graphs.- References.- Index.
£125.99
Springer An Introduction to KMS Weights
Book Synopsis
£58.49
Birkhäuser Mathematical Theory of Compressible Fluids on
Book SynopsisPreface.- Notation, definitions and basic concepts.- Equations of motion.- Barotropic viscous fluid with the Dirichlet boundary conditions.- Barotropic viscous fluid with slip boundary condition.- Weak-strong uniqueness.- Existence of strong solutions via energy methods.- Existence of strong solutions in the Lp - Lq framework.- The full system.- Index.- References.
£89.99
Springer Nonlinear Functional Analysis with Applications
Book SynopsisPreface.- Introduction and Main Results.- Part I. A Short Course in Nonlinear Functional Analysis.- Elements of Degree Theory.- Theory of Positive Mappings in Ordered Banach Spaces.- Elements of Bifurcation Theory.- Part II. Introduction to Semilinear Elliptic Problems via Semenov Approximation.- Elements of Functions Spaces.- Semilinear Hypoelliptic Robin Problems via Semenov Approximation.- Spectral Analysis of the Closed Realization A.- Local Bifurcation Theorem for Problem (6.4).- Fixed Point Theorems in Ordered Banach Spaces.- The Super-subsolution Method.- Sublinear Hypoelliptic Robin Problems.- Part III. A Combustion Problem with General Arrhenius Equations and Newtonian Cooling.- Proof of Theorem 1.5 (Existence and Uniqueness).- Proof of Theorem 1.7 (Multiplicity).- Proof of Theorem 1.9 (Unique solvability for λ sufficiently small).- Proof of Theorem 1.10 (Unique solvability for λ sufficiently large).- Proof of Theorem 1.11 (Asymptotics).- Part IV. Summary and Discussion.- Open Problems in Numerical Analysis.- Concluding Remarks.- Part V Appendix.- A The Maximum Principle for Second Order Elliptic Operators.- Bibliography.- Index.
£107.99
