Functional analysis and transforms Books
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.
£54.99
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.
£49.99
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 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 Analytic Methods of Spectral Representations of NonSelfadjoint NonUnitary Operators
Book Synopsis- 1. Local Colligations and Model Representations of Linear Non-Self-Adjoint Bounded Operators.- 2. Unitary Metric Colligations and Their Model Representations.- 3. Colligations Corresponding to Unbounded Operators and Their Model Representations.- 4. Elements of V.P. Potapov's J -Theory and the Factorization Problem of J -Contractive Matrix Functions.
£75.99
Springer Introduction to Functional Analysis
£54.99
Springer Connected Sets in Global Bifurcation Theory
Book Synopsis- 1. Introduction.- 2. Set Theory Foundations.- 3. Metric Spaces.- 4. Types of Connectedness.- 5. Congestion Points.- 6. Decomposable and Indecomposable Continua.- 7. Pathological Examples.
£43.99
Springer Fixed Points of Semigroups of Pointwise Lipschitzian Operators
Book SynopsisPreface.- Introduction.- Preliminaries.- Semigroups of nonlinear operators.- Existence of common fixed points for pointwise Lipschitzian semigroups.- Construction of common fixed points.- Applications and related topics.- Notes.- Bibliography.-Index.
£44.99
Springer Nature Switzerland AG Espaces vectoriels topologiques
£29.99
Birkhauser Verlag AG The Navier-Stokes Equations: An Elementary Functional Analytic Approach
Book SynopsisThe primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers’ convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.Trade ReviewFrom the reviews:“The book is well written and not unnecessarily wordy. There is an up-to-date bibliography and a nice index. … a mathematician who wishes to know what the important issues concerning eq. (1) are and what has been achieved, would find this an excellent source. Equally, a mathematically-minded student, with a good grounding in analysis and who has decided to work in this area, or the teacher who wants to teach a course on this material would find this a valuable text.” (P. N. Shankar,Current Science, Vol. 85 (2), July, 2003)Table of ContentsPreliminary Results.- The Stationary Navier-Stokes Equations.- The Linearized Nonstationary Theory.- The Full Nonlinear Navier-Stokes Equations.
£75.99
Springer International Publishing AG Introduction to Partial Differential Equations
Book SynopsisThis textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.Trade Review“This textbook furnishes the basis for a 1-year introductory course in partial differential equations for advanced undergraduates. … The book is written with great care and great attention to detail throughout. At the end of every chapter there are well-chosen exercises that genuinely add depth to the concepts treated in the text. … this book can be wholeheartedly recommended.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 181, 2016)“This book easily covers all the material one might want in a course aimed at first-time students of PDEs. … I recommend this one highly: It provides the best first-course introduction to a vast and ever-more relevant and active area. Students, and perhaps instructors too, will learn much from it. If they wish to go beyond the material taught in a first course, this text will prepare them better than any other I know.” (SIAM Review, Vol. 56 (3), September, 2014)“Introduction to Partial Differential Equations is a complete, well-written textbook for upper-level undergraduates and graduate students. Olver … thoroughly covers the topic in a readable format and includes plenty of examples and exercises, ranging from the typical to independent projects and computer projects. … Instructors teaching an introduction to partial differential equations course will want to consider this textbook as a viable option for their students. Summing Up: Highly Recommended. Upper-division undergraduates, graduate students, and faculty.” (S. L. Sullivan, Choice, Vol. 51 (11), July, 2014)“This introduction to partial differential equations is addressed to advanced undergraduates or graduate students … . an imposing book that includes plenty of material for two semesters even at the graduate level. … The author succeeds at maintaining a good balance between solution methods, mathematical rigor, and applications. With appropriate selection of topics this could serve for a one semester introductory course for undergraduates or a full year course for graduate students. … the author has clearly taken pains to make it readable and accessible.” (William J. Satzer, MAA Reviews, January, 2014)Table of ContentsWhat are Partial Differential Equations?.- Linear and Nonlinear Waves.- Fourier Series.- Separation of Variables.- Finite Differences.- Generalized Functions and Green’s Functions.- Complex Analysis and Conformal Mapping.- Fourier Transforms.- Linear and Nonlinear Evolution Equations.- A General Framework for Linear Partial Differential Equations.- Finite Elements and Weak Solutions.- Dynamics of Planar Media.- Partial Differential Equations in Space.
£44.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG The Analysis of Linear Partial Differential
Book SynopsisAuthor received the 1962 Fields Medal Author received the 1988 Wolf Prize (honoring achievemnets of a lifetime) Author is leading expert in partial differential equationsTrade ReviewFrom the reviews: "...these volumes are excellently written and make for greatly profitable reading. For years to come they will surely be a main reference for anyone wishing to study partial differential operators."-- MATHEMATICAL REVIEWS "This volume focuses on linear partial differential operators with constant coefficients … . Each chapter ends with notes on the literature, and there is a large bibliography. … The binding of this softcover reprint seems quite good … . Overall, it is great to have this book back at an affordable price. It really does deserve to be described as a classic." (Fernando Q. Gouvêa, MathDL, January, 2005)Table of ContentsExistence and Approximation of Solutions of Differential Equations.- Interior Regularity of Solutions of Differential Equations.- The Cauchy and Mixed Problems.- Differential Operators of Constant Strength.- Scattering Theory.- Analytic Function Theory and Differential Equations.- Convolution Equations.
£49.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Operator Algebras: Theory of C*-Algebras and von Neumann Algebras
Book SynopsisThis book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality. The presentation carefully and precisely explains the main features of each part of the theory of operator algebras; most important arguments are at least outlined and many are presented in full detail.Trade ReviewFrom the reviews: "The volume under review is supposed to cover basics on operator algebras … . Blackadar’s book is very well written and pleasant to read. It is especially suited to readers who already know the basics of operator algebras but who need a reference for some result or who wish to have a unified approach to topics treated by them." (Paul Jolissaint, Mathematical Reviews, Issue 2006 k) "This volume is an important and useful contribution to the literature on C*-algebras and von Neumann algebras. … The book is extremely well written. It can be recommended as a reference to graduate students working in operator algebra theory and to other mathematicians who want to bring themselves up-to-date on the subject." (V. M. Manuilov, Zentralblatt MATH, Vol. 1092 (18), 2006)Table of ContentsOperators on Hilbert Space.- C*-Algebras.- Von Neumann Algebras.- Further Structure.- K-Theory and Finiteness.
£151.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Infinite Dimensional Analysis: A Hitchhiker's Guide
Book SynopsisWhat you’ll find in this monograph is nothing less than a complete and rigorous study of modern functional analysis. It is intended for the student or researcher who could benefit from functional analytic methods, but who does not have an extensive background in the subject and does not plan to make a career as a functional analyst. It develops the topological structures in connection with a number of topic areas such as measure theory, convexity, and Banach lattices, as well as covering the analytic approach to Markov processes. Many of the results were previously available only in works scattered throughout the literature.Table of ContentsOdds and ends.- Topology.- Metrizable spaces.- Measurability.- Topological vector spaces.- Normed spaces.- Convexity.- Riesz spaces.- Banach lattices.- Charges and measures.- Integrals.- Measures and topology.- Lp-spaces.- Riesz Representation Theorems.- Probability measures.- Spaces of sequences.- Correspondences.- Measurable correspondences.- Markov transitions.- Ergodicity.
£85.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Infinite Dimensional Analysis: A Hitchhiker's Guide
Book SynopsisWhat you’ll find in this monograph is nothing less than a complete and rigorous study of modern functional analysis. It is intended for the student or researcher who could benefit from functional analytic methods, but who does not have an extensive background in the subject and does not plan to make a career as a functional analyst. It develops the topological structures in connection with a number of topic areas such as measure theory, convexity, and Banach lattices, as well as covering the analytic approach to Markov processes. Many of the results were previously available only in works scattered throughout the literature.Table of ContentsOdds and ends.- Topology.- Metrizable spaces.- Measurability.- Topological vector spaces.- Normed spaces.- Convexity.- Riesz spaces.- Banach lattices.- Charges and measures.- Integrals.- Measures and topology.- Lp-spaces.- Riesz Representation Theorems.- Probability measures.- Spaces of sequences.- Correspondences.- Measurable correspondences.- Markov transitions.- Ergodicity.
£59.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Espaces vectoriels topologiques: Chapitres 1à 5
Book SynopsisLes Éléments de mathématique de Nicolas Bourbaki ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce livre est le cinquième du traité ; il est consacré aux bases de l’analyse fonctionnelle. Il contient en particulier le théorème de Hahn-Banach et le théorème de Banach-Steinhaus. Il comprend les chapitres: -1. Espaces vectoriels topologiques sur un corps value; -2. Ensembles convexes et espaces localement convexes; -3. Espaces d’applications linéaires continues; -4. La dualité dans les espaces vectoriels topologiques; -5. Espaces hilbertiens (théorie élémentaire). Il contient également des notes historiques. Ce volume a été publié en 1981.Table of ContentsEspaces vectoriels topologiques sur un corps valué.- Ensembles convexes et espaces localement convexes.- Espaces d'applications linéaires continues.- La dualité dans les espaces vectoriels topologiques.- Espaces hilbertiens (théorie élémentaire).
£49.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Classification of Nuclear C*-Algebras. Entropy in Operator Algebras
Book Synopsisto the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. Afactor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.Trade ReviewFrom the reviews:"... These notes [by E.Stormer] describe the main approaches to noncommutative entropy, together with several ramifications and variants. The notion of generator and variational principle are used to give applications to subfactors and C*-algebra formalism of quantum statistical mechanics. The author considers the most frequently studied examples, including Bernoulli shifts, Bogolyubov automorphisms, dual automorphisms on crossed products, shifts on infinite free products, and binary shifts on the CAR-algebra. The mathematical techniques and ideas are beautifully exposed, and the whole paper is a rich resource on the subject, either for the expert or the beginner. ..."V.Deaconu, Mathematical Reviews 2004"... the author gives a clear presentation of the dramatic developments in the classification theory for simple C*-algebras that have taken place over the past 25 years or so. ... As there is such a large amount of literature on the subject, this monograph article is particularly useful to the relative novice who wants to know the fundamental results in the theory without wading through a massive amount of detail. ...This monograph-length article is extremely well-written, filled with concrete examples, and has an exhaustive bibliography. I recommend it as an excellent introduction to graduate students and other mathematicians who want to bring themselves up-to-date on the subject. .."J.A.Packer, Mathematical Reviews 2004“Both contributions to this volume are high-end, excellently written research reviews, reflecting very thoroughly the current status in the respectively treated subbranches of the quickly evolving complex field of C* algebra theory. They both give a beautiful lay-out of the vast research program in the field which has been going on for decades … as well as to the standard works. … an excellent, very thorough, concise and needed overview for the researcher who is active in this field.” (Mark Sioen, Bulletin of the Belgian Mathematical Society, 2007) Table of ContentsI. Classification of Nuclear, Simple C*-algebras.- II. A Survey of Noncommutative Dynamical Entropy.
£85.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Mathematical Theory of Feynman Path Integrals: An Introduction
Book SynopsisThe 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.Trade ReviewFrom the reviews of the second edition:"The second edition (from 2008) contains a large additional chapter … entitled ‘Some Recent Developments’, where alternative attempts at a rigourous formalism are presented, as well as recent applications. Summarizing, this is a good and insightful book for those familiar with path integrals and curious about the mathematic foundations of path integration." (Jacques Tempere, Belgian Physical Society Magazine, Issue 2, June, 2009)“The new edition goes way beyond the habitual corrections and additions … . It is good to have this new book. Not only for the more recent results it contains, but also as a point of departure for so many questions that are still open in the realm of infinite dimensional oscillatory integrals.” (Ludwig Streit, Zentralblatt MATH, Vol. 1222, 2011)Table of ContentsThe Fresnel Integral of Functions on a Separable Real Hilbert Space.- The Feynman Path Integral in Potential Scattering.- The Fresnel Integral Relative to a Non-singular Quadratic Form.- Feynman Path Integrals for the Anharmonic Oscillator.- Expectations with Respect to the Ground State of the Harmonic Oscillator.- Expectations with Respect to the Gibbs State of the Harmonic Oscillator.- The Invariant Quasi-free States.- The Feynman History Integral for the Relativistic Quantum Boson Field.- Some Recent Developments.
£32.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Hypergeometric Orthogonal Polynomials and Their q-Analogues
Book SynopsisThe present book is about the Askey scheme and the q-Askey scheme, which are graphically displayed right before chapter 9 and chapter 14, respectively. The fa- lies of orthogonal polynomials in these two schemes generalize the classical orth- onal polynomials (Jacobi, Laguerre and Hermite polynomials) and they have pr- erties similar to them. In fact, they have properties so similar that I am inclined (f- lowing Andrews & Askey [34]) to call all families in the (q-)Askey scheme classical orthogonal polynomials, and to call the Jacobi, Laguerre and Hermite polynomials very classical orthogonal polynomials. These very classical orthogonal polynomials are good friends of mine since - most the beginning of my mathematical career. When I was a fresh PhD student at the Mathematical Centre (now CWI) in Amsterdam, Dick Askey spent a sabbatical there during the academic year 1969–1970. He lectured to us in a very stimulating wayabouthypergeometricfunctionsandclassicalorthogonalpolynomials. Evenb- ter, he gave us problems to solve which might be worth a PhD. He also pointed out to us that there was more than just Jacobi, Laguerre and Hermite polynomials, for instance Hahn polynomials, and that it was one of the merits of the Higher Transc- dental Functions (Bateman project) that it included some newer stuff like the Hahn polynomials (see [198, §10. 23]).Trade ReviewFrom the reviews:“The book starts with a brief but valuable foreword by Tom Koornwinder on the history of the classification problem for orthogonal polynomials. … the ideal text for a graduate course devoted to the classification, and it is a valuable reference, which everyone who works in orthogonal polynomials will want to own.” (Warren Johnson, The Mathematical Association of America, August, 2010)Table of ContentsDefinitions and Miscellaneous Formulas.- Classical orthogonal polynomials.- Orthogonal Polynomial Solutions of Differential Equations.- Orthogonal Polynomial Solutions of Real Difference Equations.- Orthogonal Polynomial Solutions of Complex Difference Equations.- Orthogonal Polynomial Solutions in x(x+u) of Real Difference Equations.- Orthogonal Polynomial Solutions in z(z+u) of Complex Difference Equations.- Hypergeometric Orthogonal Polynomials.- Polynomial Solutions of Eigenvalue Problems.- Classical q-orthogonal polynomials.- Orthogonal Polynomial Solutions of q-Difference Equations.- Orthogonal Polynomial Solutions in q?x of q-Difference Equations.- Orthogonal Polynomial Solutions in q?x+uqx of Real
£104.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Field Theory III: Gauge Theory: A Bridge between Mathematicians and Physicists
Book SynopsisIn this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a ParadigmPart II: Ariadne's Thread in Gauge TheoryPart III: Einstein's Theory of Special RelativityPart IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos). Trade ReviewFrom the reviews:“This book is the third volume of a complete exposition of the important mathematical methods used in modern quantum field theory. It presents the very basic formalism, important results, and the most recent advances emphasizing the applications to gauge theory. … the book’s greatest strength is Zeidler’s zeal to help students understand fundamental mathematics better. I thus find the book extremely useful since it signifies the role of mathematics for the road to reality … .” (Gert Roepstorff, Zentralblatt MATH, Vol. 1228, 2012)“The present book is a good companion to the literature on the subject of the volume title, especially for those already familiar with it. … the book touches upon a large number of subjects on the interface between mathematics and physics, providing a good overview of gauge theory in both fields. It contains lots of background material, many historical remarks, and an extensive bibliography that helps the interested reader to continue his or her more thorough studies elsewhere.” (Walter D. van Suijlekom, Mathematical Reviews, Issue 2012 m)Table of ContentsPrologue.- Part I. The Euclidean Manifold as a Paradigm: 1. The Euclidean Space E3 (Hilbert Space and Lie Algebra Structure).- 2. Algebras and Duality (Tensor Algebra, Grassmann Algebra, Cli_ord Algebra, Lie Algebra).- 3. Representations of Symmetries in Mathematics and Physics.- 4. The Euclidean Manifold E3.- 5. The Lie Group U(1) as a Paradigm in Harmonic Analysis and Geometry.- 6. Infinitesimal Rotations and Constraints in Physics.- 7. Rotations, Quaternions, the Universal Covering Group, and the Electron Spin.- 8. Changing Observers - A Glance at Invariant Theory Based on the Principle of the Correct Index Picture.- 9. Applications of Invariant Theory to the Rotation Group.- 10. Temperature Fields on the Euclidean Manifold E3.- 11. Velocity Vector Fields on the Euclidean Manifold E3.- 12. Covector Fields and Cartan's Exterior Differential - the Beauty of Differential Forms.- Part II. Ariadne's Thread in Gauge Theory: 13. The Commutative Weyl U(1)-Gauge Theory and the Electromagnetic Field.- 14. Symmetry Breaking.- 15. The Noncommutative Yang{Mills SU(N)-Gauge Theory.- 16. Cocycles and Observers.- 17. The Axiomatic Geometric Approach to Bundles.- Part III. Einstein's Theory of Special Relativity: 18. Inertial Systems and Einstein's Principle of Special Relativity.- 19. The Relativistic Invariance of the Maxwell Equations.- 20. The Relativistic Invariance of the Dirac Equation and the Electron Spin.- Part IV. Ariadne's Thread in Cohomology: 21. The Language of Exact Sequences.- 22. Electrical Circuits as a Paradigm in Homology and Cohomology.- 23. The Electromagnetic Field and the de Rham Cohomology.- Appendix.- Epilogue.- References.- List of Symbols.- Index
£189.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Elliptic Functions
Book SynopsisThis book has grown out of a course of lectures on elliptic functions, given in German, at the Swiss Federal Institute of Technology, Zurich, during the summer semester of 1982. Its aim is to give some idea of the theory of elliptic functions, and of its close connexion with theta-functions and modular functions, and to show how it provides an analytic approach to the solution of some classical problems in the theory of numbers. It comprises eleven chapters. The first seven are function-theoretic, and the next four concern arithmetical applications. There are Notes at the end of every chapter, which contain references to the literature, comments on the text, and on the ramifications, old and new, of the problems dealt with, some of them extending into cognate fields. The treatment is self-contained, and makes no special demand on the reader's knowledge beyond the elements of complex analysis in one variable, and of group theory.Trade Review"...In the breadth, depth and inevitability of treatment of this beautiful material, the author has made a contribution to the mathematical community consistent with the distinction of his career. That he has succeeded in compressing this treatment into a succinct monograph of fewer than 190 pages is a testament to his taste, discipline and powers of exposition."-- MATHEMATICAL REVIEWSTable of ContentsI. Periods of meromorphic functions.- § 1. Meromorphic functions.- § 2. Periodic meromorphic functions.- § 3. Jacobi’s lemma.- § 4. Elliptic functions.- § 5. The modular group and modular functions.- Notes on Chapter I.- II. General properties of elliptic functions.- §1. The period parallelogram.- § 2. Elementary properties of elliptic functions.- Notes on Chapter II.- III. Weierstrass’s elliptic function ?(z).- §1. The convergence of a double series.- § 2. The elliptic function ?(z).- § 3. The differential equation associated with ?(z).- § 4. The addition-theorem.- § 5. The generation of elliptic functions.- Appendix I. The cubic equation.- Appendix II. The biquadratic equation.- Notes on Chapter III.- IV. The zeta-function and the sigma-function of Weierstrass.- § 1. The function ?(z).- §2. The function ?(z).- § 3. An expression for elliptic functions.- Notes on Chapter IV.- V. The theta-functions.- §1. The function ?(?, ?).- § 2. The four sigma-functions.- § 3. The four theta-functions.- § 4. The differential equation.- § 5. Jacobi’s formula for ?’ (0, ?).- § 6. The infinite products for the theta-functions.- § 7. Theta-functions as solutions of functional equations.- § 8. The transformation formula connecting ?3(v, ?) and ?3(?, ?1/?) ..- Notes on Chapter V.- VI. The modular function J(?).- § 1. Definition of J(?).- § 2. The functions g2(?) and g3(?).- § 3. Expansion of the function J(?) and the connexion with theta-functions.- § 4. The function J(?) in a fundamental domain of the modular group ..- § 5. Relations between the periods and the invariants of ?(u).- § 6. Elliptic integrals of the first kind.- Notes on Chapter VI.- VII. The Jacobian elliptic functions and the modular function ?(?).- § 1. The functions sn u, en u, dn u of Jacobi.- § 2. Definition by theta-functions.- § 3. Connexion with the sigma-functions.- § 4. The differential equation.- § 5. Infinite products for the Jacobian elliptic functions.- § 6. Addition-theorems for sn u, cn u, dn u.- § 7. The modular function ?(?).- §8. Mapping properties of ?(?) and Picard’s theorem.- Notes on Chapter VII.- VIII. Dedekind’s ?-function and Euler’s theorem on pentagonal numbers.- § 1. Connexion with the invariants of the ?-function and with the theta-functions.- § 2. Euler’s theorem and Jacobi’s proof.- § 3. The transformation formula connecting ?(z) and ?(?½).- §4. Siegel’s proof of Theorem 1.- §5. Connexion between ?(z) and the modular functions J(z), ?(z).- Notes on Chapter VIII.- IX. The law of quadratic reciprocity.- § 1. Reciprocity of generalized Gaussian sums.- § 2. Quadratic residues.- §3. The law of quadratic reciprocity.- Notes on Chapter IX.- X. The representation of a number as a sum of four squares ..- §1. The theorems of Lagrange and of Jacobi.- § 2. Proof of Jacobi’s theorem by means of theta-functions.- §3. Siegel’s proof of Jacobi’s theorem.- Notes on Chapter X.- XI. The representation of a number by a quadratic form.- §1. Positive-definite quadratic forms.- § 2. Multiple theta-series and quadratic forms.- § 3. Theta-functions associated to positive-definite forms.- § 4. Representation of an even integer by a positive-definite form.- Notes on Chapter XI.- Chronological table.
£54.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Normed Linear Spaces
Table of ContentsI. Linear Spaces.- II. Normed Linear Spaces.- III. Completeness, Compactness, and Reflexivity.- IV. Unconditional Convergence and Bases.- V. Compact Convex Sets and Continuous Function Spaces.- VI. Norm and Order.- VII. Metric Geometry in Normed Spaces.- VIII. Reader’s Guide.- Index of Citations.- Index of Symbols.
£44.99
Birkhauser Verlag AG The Functional Calculus for Sectorial Operators
Book SynopsisThis book contains a systematic and partly axiomatic treatment of the holomorphic functional calculus for unbounded sectorial operators. The account is generic so that it can be used to construct and interrelate holomorphic functional calculi for other types of unbounded operators. Particularly, an elegant unified approach to holomorphic semigroups is obtained. The last chapter describes applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis.Table of ContentsAxiomatics for Functional Calculi.- The Functional Calculus for Sectorial Operators.- Fractional Powers and Semigroups.- Strip-type Operators and the Logarithm.- The Boundedness of the H?-Calculus.- Interpolation Spaces.- The Functional Calculus on Hilbert Spaces.- Differential Operators.- Mixed Topics.
£85.49
£16.57
Springer Noncommutative Probability
Book SynopsisThe intention of this book is to explain to a mathematician having no previous knowledge in this domain, what "noncommutative probability" is. So the first decision was not to concentrate on a special topic. For different people, the starting points of such a domain may be different. In what concerns this question, different variants are not discussed. One such variant comes from Quantum Physics. The motivations in this book are mainly mathematical; more precisely, they correspond to the desire of developing a probability theory in a new set-up and obtaining results analogous to the classical ones for the newly defined mathematical objects. Also different mathematical foundations of this domain were proposed. This book concentrates on one variant, which may be described as "von Neumann algebras". This is true also for the last chapter, if one looks at its ultimate aim. In the references there are some papers corresponding to other variants; we mention Gudder, S.P. &al (1978). Segal, I.E. (1965) also discusses "basic ideas".Table of ContentsPreface. 1. Central limit theorem on L(H). 2. Probability theory on von Neumann algebras. 3. Free independence. 4. The Clifford algebra. 5. Stochastic integrals. 6. Conditional mean values. 7. Jordan algebras. References. Index.
£85.49
Springer Verlag, Singapore Geometry of Deep Learning: A Signal Processing Perspective
Book SynopsisThe focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems.Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.Trade Review“This book is based on material that has been prepared for senior-level undergraduate classes, this book can be used for one-semester senior-level undergraduate and graduate-level classes.” (Arzu Ahmadova, zbMATH 1493.68003, 2022)Table of ContentsPart I Basic Tools for Machine Learning: 1. Mathematical Preliminaries.- 2. Linear and Kernel Classifiers.- 3. Linear, Logistic, and Kernel Regression.- 4. Reproducing Kernel Hilbert Space, Representer Theorem.- Part II Building Blocks of Deep Learning: 5. Biological Neural Networks.- 6. Artificial Neural Networks and Backpropagation.- 7. Convolutional Neural Networks.- 8. Graph Neural Networks.- 9. Normalization and Attention.- Part III Advanced Topics in Deep Learning.- 10. Geometry of Deep Neural Networks.- 11. Deep Learning Optimization.- 12. Generalization Capability of Deep Learning.- 13. Generative Models and Unsupervised Learning.- Summary and Outlook.- Bibliography.- Index.
£37.49
Springer-Verlag GmbH Generalized Functions Method in Boundary Value Problems for Wave Equations
£116.99
Springer Banach Contraction Principle
£132.99
Springer Topological FixedPoint Theory in Suitable Banach
Book SynopsisTopological Structures.- Fixed-Point Theory in Suitable Banach Algebras.- Fixed-Point Theory for Block Operator Matrices.- Nonlinear One-Dimensional Boundary-Value Problems.- Two-Dimensional Boundary-Value Problems.- Existence Theory of Critical-Type of Fixed Point.- Two-Dimensional Value Problems for Differential Inclusion.
£123.49
Springer Real Analysis Methods for Markov Processes
Book SynopsisIntroduction and Main Results.- Elements of Functional Analysis.- Elements of Measure Theory and Lp Spaces.- Elements of Real Analysis.- Harmonic Functions and Poisson Integrals.- Besov Spaces via Poisson Integrals.- Sobolev and Besov Spaces.- Maximum Principles in Sobolev Spaces.- Elements of Singular Integrals.- CalderonZygmund Kernels and Their Commutators.- CalderonZygmund Variable Kernels and Their Commutators.- Dirichlet Problems in Sobolev Spaces.- CalderonZygmund Kernels and Interior Estimates.- CalderonZygmund Kernels and Boundary Estimates.- Unique Solvability of the Homogeneous Dirichlet Problem.- Regular Oblique Derivative Problems in Sobolev Spaces.- Oblique Derivative Boundary Conditions.- Boundary Representation Formula for Solutions.- Boundary Regularity of Solutions.- Proof of Theorems 16.1 and 16.2.- Markov Processes and Feller Semigroups.- Feller Semigroups with Dirichlet Condition.- Feller Semigroups with an Oblique Derivative Condition.- Feller Semigroups and Bo
£151.99
Springer Trace Inequalities
Book SynopsisChapter 1 Fundamentals of Matrices and Operators.- Chapter 2 Unitarily Invariant Norms and Inequalities.- Chapter 3 Trace Inequalities for Positive Semidefinite Matrices.- Chapter 4 Norm Inequalities for Positive Semidefinite Matrices.- Chapter 5 Positive Maps and Operator Means.
£142.49
Springer Symbolic Dynamical Systems and CAlgebras
Book SynopsisIntroduction.- Topological Markov Shifts.- Flow Equivalence.- Continuous Orbit Equivalence.- Etale Groupoids and CuntzKrieger Algebras.- K-Theory for In?nite Simple ??*-Algebras.- K-Theory for CuntzKrieger Algebras.- Strong Shift Equivalence, Flow Equivalence and CuntzKrieger Algebras.- Classi?cation Theorem for Continuous Orbit Equivalence.- Gauge Actions and Continuous Orbit Equivalence.- Classi?cation Theorem for Flow Equivalence and Topological Conjugacy.
£142.49
Springer Applied Functional Analysis
Book SynopsisChapter 1. Operator Theory.- Chapter 2. Distribution Theory.- Chapter 3. Theory of Sobolev Spaces.- Chapter 4. Elliptic Theory.- Chapter 5. Calculus of Variations.
£66.49
Independently Published Modern Mathemagics
£20.17
Amazon Digital Services LLC - Kdp Triumph of Love Illustrated Part I
£21.22
Amazon Digital Services LLC - Kdp Triumph of Love Illustrated Part II
£29.75
Springer-Verlag New York Inc. The Mathematical Theory of Finite Element Methods
Book SynopsisIt can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory.Trade ReviewSecond Edition S.C. Brenner and L.R. Scott The Mathematical Theory of Finite Element Methods "[This is] a well-written book. A great deal of material is covered, and students who have taken the trouble to master at least some of the advanced material in the later chapters would be well placed to embark on research in the area." ZENTRALBLATT MATH From the reviews of the third edition: "An excelent survey of the deep mathematical roots of finite element methods as well as of some of the newest and most formal results concerning these methods. … The approach remains very clear and precise … . A significant number of examples and exercises improve considerably the accessability of the text. The authors also point out different ways the book could be used in various courses. … valuable reference and source for researchers (mainly mathematicians) in the topic." (Calin Ioan Gheorghiu, Zentralblatt MATH, Vol. 1135 (13), 2008)Table of ContentsPreface(3rdEd).- Preface(2ndEd).- Preface(1stED).- Basic Concepts.- Sobolev Spaces.- Variational Formulation of Elliptic Boundary Value Problems.- The Construction of a Finite Element of Space.- Polynomial Approximation Theory in Sobolev Spaces.- n-Dimensional Variational Problems.- Finite Element Multigrid Methods.- Additive Schwarz Preconditioners.- Max-norm Estimates.- Adaptive Meshes.- Variational Crimes.- Applications to Planar Elasticity.- Mixed Methods.- Iterative Techniques for Mixed Methods.- Applications of Operator-Interpolation Theory.- References.- Index.
£75.99
Springer London An Introduction to Laplace Transforms and Fourier Series Springer Undergraduate Mathematics Series
Book SynopsisAn Introduction to Laplace Transforms and Fourier Series will be useful for second and third year undergraduate students in engineering, physics or mathematics, as well as for graduates in any discipline such as financial mathematics, econometrics and biological modelling requiring techniques for solving initial value problems.Table of ContentsThe Laplace Transform.- Further Properties of the Laplace Transform.- Convolution and the Solution of Ordinary Differential Equations.- Fourier Series.- Partial Differential Equations.- Fourier Transforms.- Wavelets and Signal Processing.- Complex Variables and Laplace Transforms.
£34.19
Springer International Publishing AG Regular Functions of a Quaternionic Variable
Book SynopsisThis book surveys the foundations of the theory of slice regular functions over the quaternions, introduced in 2006, and gives an overview of its generalizations and applications.As in the case of other interesting quaternionic function theories, the original motivations were the richness of the theory of holomorphic functions of one complex variable and the fact that quaternions form the only associative real division algebra with a finite dimension n>2. (Slice) regular functions quickly showed particularly appealing features and developed into a full-fledged theory, while finding applications to outstanding problems from other areas of mathematics. For instance, this class of functions includes polynomials and power series. The nature of the zero sets of regular functions is particularly interesting and strictly linked to an articulate algebraic structure, which allows several types of series expansion and the study of singularities. Integral representation formulas enrich the theory and are fundamental to the construction of a noncommutative functional calculus. Regular functions have a particularly nice differential topology and are useful tools for the construction and classification of quaternionic orthogonal complex structures, where they compensate for the scarcity of conformal maps in dimension four.This second, expanded edition additionally covers a new branch of the theory: the study of regular functions whose domains are not axially symmetric. The volume is intended for graduate students and researchers in complex or hypercomplex analysis and geometry, function theory, and functional analysis in general.Table of ContentsIntroduction.- 1.Definitions and Basic Results.- 2.Regular Power Series.- 3.Zeros.- 4.Infinite Products.- 5.Singularities.- 6.Integral Representations.- 7.Maximum Modulus Theorem and Applications.- 8.Spherical Series and Differential.- 9.Fractional Transformations and the Unit Ball.- 10.Generalizations.- 11. Function Theory over Non-symmetric Slice Domains.-12. Applications.- Bibliography.- Index.
£80.99
Springer-Verlag GmbH Homogenisation of Laminated Metamaterials and the Inner Spectrum
£37.99
LAP Lambert Academic Publishing Algebra i kombinatorika v teorii gladkikh prodolzheniy
£29.81
Springer Fachmedien Wiesbaden Spektraltheorie selbstadjungierter Operatoren im Hilbertraum und elliptischer Differentialoperatoren
Book SynopsisIn diesem Lehrbuch wird der Spektralsatz für selbstadjungierte Operatoren aus dem Resultat der Linearen Algebra über die Diagonalisierung Hermitescher Matrizen hergeleitet. Dabei werden Lebesgue-Stieltjes-Integrale verwendet und der Auswahl- sowie der Konvergenzsatz von Helly über monotone Funktionen bereitgestellt. Wir konstruieren die Spektralschar durch eine technisch aufwändige Approximation, wobei die Stieltjes-Umkehrformel im Zentrum des Beweises steht. Ein Ergebnis hiervon ist, dass selbstadjungierte Operatoren nicht nur ein diskretes, sondern auch ein kontinuierliches Spektrum besitzen. Die auftretenden Streueigenwerte können hierbei nicht durch Variationsmethoden gewonnen werden. Dann wenden wir uns der zentralen Frage zu, welche elliptischen Differentialoperatoren eine selbstadjungierte Fortsetzung besitzen und somit im Geltungsbereich des Spektralsatzes liegen. Hier unterscheiden wir zwischen stabilen elliptischen Differentialoperatoren auf beschränkten Gebieten und denen auf dem ganzen Raum, wie etwa dem Schrödingeroperator. Auch Laplace-Beltrami-Operatoren und der Schwarzsche Operator für Minimalflächen werden im obigen Sinne als selbstadjungiert erkannt. Am Ende dieses Buches geben wir eine Einführung in die Störungstheorie selbstadjungierter Operatoren. Hier weisen wir die analytische Abhängigkeit der Spektralschar vom Störungsparameter nach.Dieses Werk zur Spektraltheorie ist insbesondere für das fortgeschrittene Mathematik- und Physikstudium geeignet, Kenntnisse in der Funktionalanalysis und der Theorie elliptischer Differentialgleichungen werden vorausgesetzt.Table of ContentsAbgeschlossene Operatoren mit ihren Graphen.- Stabile elliptische Differentialoperatoren auf beschränkten Gebieten.- Ausschöpfung des Hilbertraums durch Niveauräume des Differentialoperators.- Über die Selbstadjungiertheit von Hermiteschen Operatoren.- Die Resolvente eines selbstadjungierten Operators.- Die Spektralschar mit ihrem Riemann-Stieltjes-Integral.- Lebesgue-Stieltjes-Integrale bezüglich der Spektralschar.- Unbeschränkte Spektraloperatoren.-Auswahl- und Konvergenzsatz von E. Helly.- Cauchy-Stieltjes-Integrale und die Stieltjes-Umkehrformel.- Approximation der Spektralschar selbstadjungierter Operatoren.- Der Spektralsatz selbstadjungierter Operatoren und ihr Spektrum.- Die Cayley-Transformierten abgeschlossener Hermitescher Operatoren.- Der Spektralsatz für unitäre Operatoren.- Die zeitabhängige Schrödingergleichung.- Die Friedrichs-Fortsetzung halbbeschränkter Hermitescher Operatoren.- Der Vergleich von Rellichoperatoren mit ihren Spektren.- Positive Laplace-Beltrami-Operatoren auf beliebigen Gebieten.- Der Operator von H.A. Schwarz für Minimalfächen.- Spektraltheorie von Schrödingeroperatoren mit halbbeschränktem Potential.- Die wesentliche Selbstadjungiertheit von Schrödingeroperatoren.- Spektraltheorie der Integraloperatoren.- Der Spektralsatz für kompakte Operatoren.- Die Integralformel von Herglotz und ihre Folgerungen.- Einführung in die Störungstheorie selbstadjungierter Operatoren.- Ein analytischer Störungssatz für die Spektralschar.
£19.99
Taylor & Francis Ltd Generalized Harmonic Analysis and Wavelet
Book SynopsisThe book presents a more comprehensive treatment of transmutation operators associated with the Bessel operator, and explores many of their properties. They are fundamental in the complete study of the Bessel harmonic analysis and the Bessel wavelet packets. Many applications of these theories and their generalizations have been injected throughout the text by way of a rich collection of problems and references. The results and methods in this book should be of interest to graduate and researchers working in special functions such as Fourier analysis, hypergroup and operator theories, differential equations, probability theory and mathematical physics. Background materials are given in adequate detail to enable a graduate student to proceed rapidly from the very basics of the frontier of research in the area of generalized harmonic analysis and wavelets.Table of ContentsThe book presents a more comprehensive treatment of transmutation operators associated with the Bessel operator, and explores many of their properties. They are fundamental in the complete study of the Bessel harmonic analysis and the Bessel wavelet packets. Many applications of these theories and their generalizations have been injected throughout the text by way of a rich collection of problems and references. The results and methods in this book should be of interest to graduate and researchers working in special functions such as Fourier analysis, hypergroup and operator theories, differential equations, probability theory and mathematical physics. Background materials are given in adequate detail to enable a graduate student to proceed rapidly from the very basics of the frontier of research in the area of generalized harmonic analysis and wavelets.
£115.00
World Scientific Publishing Co Pte Ltd Mathematics For Engineers Volume 1 Numbers And
Book SynopsisThe Karlsruhe University of Applied Sciences started an English-language Bachelor's program in Electrical Engineering in 2021. In order to support our international students with appropriate material, this three-volume textbook was written. Taking into account that different students will attend different mathematics courses, we decided to design three volumes of a series of mathematics books, each part for a single semester.Mathematical terms are clearly motivated, systematically equated and visualized in many animations. Mathematical proofs are almost completely renounced. Instead, a lot of applications support not only the application of mathematics but also contribute to a better understanding of mathematics.Important formulas and statements are clearly highlighted in order to increase the readability of the books. More than 300 images and sketches support the character of modern textbooks. The color-coded layout provides a clear overview of the presentation of the content, e.g. by adding new terms and definitions in light grey, important statements and sentences in grey.
£52.25
John Wiley & Sons Inc Theoretical Foundations of Functional Data
Book Synopsis?? Provides a concise but rigorous account of the theoretical background of FDA. ?? Introduces topics in various areas of mathematics, probability and statistics from the perspective of FDA. ?? Presents a systematic exposition of the fundamental statistical issues in FDA.Table of ContentsPreface xi 1 Introduction 1 1.1 Multivariate analysis in a nutshell 2 1.2 The path that lies ahead 13 2 Vector and function spaces 15 2.1 Metric spaces 16 2.2 Vector and normed spaces 20 2.3 Banach and Lp spaces 26 2.4 Inner Product and Hilbert spaces 31 2.5 The projection theorem and orthogonal decomposition 38 2.6 Vector integrals 40 2.7 Reproducing kernel Hilbert spaces 46 2.8 Sobolev spaces 55 3 Linear operator and functionals 61 3.1 Operators 62 3.2 Linear functionals 66 3.3 Adjoint operator 71 3.4 Nonnegative, square-root, and projection operators 74 3.5 Operator inverses 77 3.6 Fréchet and Gâteaux derivatives 83 3.7 Generalized Gram–Schmidt decompositions 87 4 Compact operators and singular value decomposition 91 4.1 Compact operators 92 4.2 Eigenvalues of compact operators 96 4.3 The singular value decomposition 103 4.4 Hilbert–Schmidt operators 107 4.5 Trace class operators 113 4.6 Integral operators and Mercer’s Theorem 116 4.7 Operators on an RKHS 123 4.8 Simultaneous diagonalization of two nonnegative definite operators 126 5 Perturbation theory 129 5.1 Perturbation of self-adjoint compact operators 129 5.2 Perturbation of general compact operators 140 6 Smoothing and regularization 147 6.1 Functional linear model 147 6.2 Penalized least squares estimators 150 6.3 Bias and variance 157 6.4 A computational formula 158 6.5 Regularization parameter selection 161 6.6 Splines 165 7 Random elements in a Hilbert space 175 7.1 Probability measures on a Hilbert space 176 7.2 Mean and covariance of a random element of a Hilbert space 178 7.3 Mean-square continuous processes and the Karhunen–Lòeve Theorem 184 7.4 Mean-square continuous processes in L2 (E,B(E), mu) 190 7.5 RKHS valued processes 195 7.6 The closed span of a process 198 7.7 Large sample theory 203 8 Mean and covariance estimation 211 8.1 Sample mean and covariance operator 212 8.2 Local linear estimation 214 8.3 Penalized least-squares estimation 231 9 Principal components analysis 251 9.1 Estimation via the sample covariance operator 253 9.2 Estimation via local linear smoothing 255 9.3 Estimation via penalized least squares 261 10 Canonical correlation analysis 265 10.1 CCA for random elements of a Hilbert space 267 10.2 Estimation 274 10.3 Prediction and regression 281 10.4 Factor analysis 284 10.5 MANOVA and discriminant analysis 288 10.6 Orthogonal subspaces and partial cca 294 11 Regression 305 11.1 A functional regression model 305 11.2 Asymptotic theory 308 11.3 Minimax optimality 318 11.4 Discretely sampled data 321 References 327 Index 331 Notation Index 334
£62.65
John Wiley & Sons Inc The Hilbert Transform of Schwartz Distributions
Book SynopsisThis book provides a modern and up-to-date treatment of the Hilberttransform of distributions and the space of periodic distributions.Taking a simple and effective approach to a complex subject, thisvolume is a first-rate textbook at the graduate level as well as anextremely useful reference for mathematicians, applied scientists,and engineers. The author, a leading authority in the field, shares with thereader many new results from his exhaustive research on the Hilberttransform of Schwartz distributions. He describes in detail how touse the Hilbert transform to solve theoretical and physicalproblems in a wide range of disciplines; these include aerofoilproblems, dispersion relations, high-energy physics, potentialtheory problems, and others. Innovative at every step, J. N. Pandey provides a new definitionfor the Hilbert transform of periodic functions, which isespecially useful for those working in the area of signalprocessing for computational purposes. This definiTable of ContentsThe Riemann-Hilbert Problem. The Hilbert Transform of Distributions in D'Lp, 1 p infinity. The Hilbert Transform of Schwartz Distributions. n-Dimensional Hilbert Transform. Further Applications of the Hilbert Transform, the HilbertProblem-- A Distributional Approach. Periodic Distributions, Their Hilbert Transform andApplications. Bibliography. Indexes.
£160.16
John Wiley & Sons Inc Fourier Series and Optical Transform Techniques
Book SynopsisFourier Series and Optical Transform Techniques in ContemporaryOptics An Introduction For anyone new to Fourier methods, this remarkable book willilluminate the subject like no other currently available. With over280 illustrations generated by computer graphics, it depicts in3-space (rather than the usual 2-space) the many basic functions ofoptical diffraction and imaging. These mind-stretchingvisualizations give the reader an enhanced understanding of bothFourier transform techniques and key principles in optics. At thesame time, the author provides a lucid text that covers wavenotation, the Fourier analysis of signals, the processing of lightin diffraction phenomena and imaging, Zernicke polynomials, Fouriertransforms for Fresnel diffraction, laser beacon adaptive optics,and related topics. Ideal for self-teaching, this book is highly recommended forworking engineers, technical staff, students of physical optics andsignal analysis, and Fourier novices in alTable of ContentsPartial table of contents: Some of the How and Why of Fourier Analysis. Fourier Series and Spectra in One-Dimension for Functions of FinitePeriod. Fourier Series and Spectra for Functions of Infinite Period; One Dimensional. Fourier Spectra for Non-Periodic Functions; One-Dimensional. The Diffraction of Light and Fourier Transforms in TwoDimensions. A Brief Summary of Linear Systems Theory Applied to OpticalImaging. Fourier Optical Transformations by Computer. Apodization and Super-Resolution, Phase from Shift, and MultipleApertures. Complex Apertures. Operations in the Fourier Transform Plane. Other Interesting and Related Topics. References. A Selected Bibliography. Index.
£155.66
John Wiley & Sons Inc Vector Integration 48 Pure and Applied
Book SynopsisA breakthrough approach to the theory and applications of stochastic integration The theory of stochastic integration has become an intensely studied topic in recent years, owing to its extraordinarily successful application to financial mathematics, stochastic differential equations, and more.Trade Review"...an important tool...gives the newest results in this field...shows an important application of vector integration..." (Bulletin of the Belgian Mathematical Society, Vol 11(1), 2004) "...it can be expected that...just like the author's 1967 volume, this book will stimulate further research on vector stochastic integration and can serve as a graduate-level reference work." (Mathematical Reviews Issue 2001h) "Dense, detailed, comprehensive introduction. Contains...material only found before in journals..." (American Mathematical Monthly, March 2002) "...a highly technical book." (The Mathematical Gazette, March 2002) "The author of this important and interesting book is a well-known specialist on vector measures." (Zentralblatt Math, Vol.974, No. 24 2001)Table of ContentsVector Integration. The Stochastic Integral. Martingales. Processes with Finite Variation. Processes with Finite Semivariation. The Itô Formula. Stochastic Integration in the Plane. Two-Parameter Martingales. Two-Parameter Processes with Finite Variation. Two-Parameter Processes with Finite Semivariation. References.
£170.06
