Functional analysis and transforms Books

Book SynopsisThis volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10–12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday. The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate.Table of ContentsPreface; My Thanks to Mourad Ismail for His Work (Richard Askey); Binomial Andrews–Gordon–Bressoud Identities (Dennis Stanton); Symmetric Expansions of Very Well Poised Basic Hypergeometric Series (George E Andrews); A Sturm–Liouville Theory for Hahn Difference Operator (A H Annaby, A E Hamza and S D Makharesh); Solvability of the Hankel Determinant Problem for Real Sequences (Andrew Bakan and Christian Berg); Convolution and Product Theorems for the Special Affine Fourier Transform (Ayush Bhandari and Ahmed I Zayed); A Further Look at Time-and-Band Limiting for Matrix Orthogonal Polynomials (M Castro, F A Grünbaum, I Pacharoni and I Zurrián); The Orthogonality of Al–Salam–Carlitz Polynomials for Complex Parameters (Howard S Cohl, Roberto S Costas-Santos and Wenqing Xu); Crouching AGM, Hidden Modularity (Shaun Cooper, Jesús Guillera, Armin Straub and Wadim Zudilin); Asymptotics of Orthogonal Polynomials and the Painlevé Transcendents (Dan Dai); From Gaussian Circle Problem to Multivariate Shannon Sampling (W Freeden, M Z Nashed); Weighted Partition Identities and Divisor Sums (F G Garvan); On the Ismail–Letessier–Askey Monotonicity Conjecture for Zeros of Ultraspherical Polynomials (Walter Gautschi); A Discrete Top-Down Markov Problem in Approximation Theory (Walter Gautschi); Supersymmetry of the Quantum Rotor (Vincent X Genest, Luc Vinet, Guo-Fu Yu and Alexei Zhedanov); The Method of Brackets in Experimental Mathematics (Ivan Gonzalez, Karen Kohl, Lin Jiu and Victor H Moll); Balanced Modular Parameterizations (Tim Huber, Danny Lara and Esteban Melendez); Some Smallest Parts Functions from Variations of Bailey's Lemma (Chris Jennings-Shaffer); Dual Addition Formulas Associated with Dual Product Formulas (Tom H Koornwinder); Holonomic Tools for Basic Hypergeometric Functions (Christoph Koutschan and Peter Paule); A Direct Evaluation of an Integral of Ismail and Valent (Alexey Kuznetsov); Algebraic Generating Functions for Gegenbauer Polynomials (Robert S Maier); q-Analogues of Two Product Formulas of Hypergeometric Functions by Bailey (Michael J Schlosser); Asymptotics of Generalized Hypergeometric Functions (Y Lin and R Wong); Mock Theta-Functions of the Third Order of Ramanujan in Terms of Appell–Lerch Series (Changgui Zhang); On Certain Positive Semidefinite Matrices of Special Functions (Ruiming Zhang);

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Book SynopsisThe book presents a theory of abstract duality pairs which arises by replacing the scalar field by an Abelian topological group in the theory of dual pair of vector spaces. Examples of abstract duality pairs are vector valued series, spaces of vector valued measures, spaces of vector valued integrable functions, spaces of linear operators and vector valued sequence spaces. These examples give rise to numerous applications such as abstract versions of the Orlicz-Pettis Theorem on subseries convergent series, the Uniform Boundedness Principle, the Banach-Steinhaus Theorem, the Nikodym Convergence theorems and the Vitali-Hahn-Saks Theorem from measure theory and the Hahn-Schur Theorem from summability. There are no books on the current market which cover the material in this book. Readers will find interesting functional analysis and the many applications to various topics in real analysis.

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Book SynopsisSome problems in mathematical analysis (e.g., in theory of function spaces, in approximation theory or in interpolation theory) lead to the investigation of weighted inequalities on certain classes of quasiconcave functions on the interval I=(a,b) ∊ R. In this book we analyse the class Qρ(I) of ρ-quasiconcave functions in a complete generality in order to establish results needed for a comprehensive study of weighted inequalities on the class Qρ(I). We illustrate our results on weighted inequalities of Hardy type, on weighted inequalities of Hardy type involving supremum, and on reverse forms of these inequalities.

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Book SynopsisThis text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators.Table of ContentsNormed Linear and Banach Spaces; Linear Operators; Quotient Spaces; Finite Dimensional Normed Spaces; Inner Product and Hilbert Spaces; The Hahn-Banach Theorem; Applications of the Hahn-Banach Theorem to Normed Spaces; The Uniform Boundedness Principle; Weak Convergence; The Open Mapping and Closed Graph Theorems; Projections; Schauder Basis; Transpose and Adjoints of Continuous Linear Operators; Compact Operators; The Fredholm Alternative; The Spectrum of an Operator; Subdivisions of the Spectrum; The Spectrum of a Compact Operator; Symmetric Linear Operators; The Spectral Theorem for Compact Symmetric Operators; Symmetric Operators with Compact Inverse; Bounded Self Adjoint Operators; Orthogonal Projections; Sesquilinear Functionals; The Spectral Theorem for Bounded Self Adjoint Operators; An Operational Calculus.

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Book SynopsisThis book (Vista II), is a sequel to Vistas of Special Functions (World Scientific, 2007), in which the authors made a unification of several formulas scattered around the relevant literature under the guiding principle of viewing them as manifestations of the functional equations of associated zeta-functions. In Vista II, which maintains the spirit of the theory of special functions through zeta-functions, the authors base their theory on a theorem which gives some arithmetical Fourier series as intermediate modular relations — avatars of the functional equations. Vista II gives an organic and elucidating presentation of the situations where special functions can be effectively used. Vista II will provide the reader ample opportunity to find suitable formulas and the means to apply them to practical problems for actual research. It can even be used during tutorials for paper writing.Table of ContentsBernoulli and Allied Polynomials; Chebyshev Polynomials and Energy Levels of Carbon Hydrates; The Gamma Function Continued - Kummer's Fourier Series, The Stirling Formulas, Etc.; The Hurwitz-Lerch Zeta-Function; The Dirichlet L-Function; Arithmetical Fourier Series; The Madelung Constants and Special Functions; Applications of Fourier Series - Parseval Identity; The Derivative of Dirichlet L-Function and the Kronecker Limit Formula.

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Book SynopsisThe book provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical properties of triangles in normed spaces. Since the appearance of Jordan-von Neumann's classical theorem (The Parallelogram Law) in 1935, the field of characterizations of inner product spaces has received a significant amount of attention in various literature texts. Moreover, the techniques arising in the theory of functional equations have shown to be extremely useful in solving key problems in the characterizations of Banach spaces as Hilbert spaces.This book presents, in a clear and detailed style, state-of-the-art methods of characterizing inner product spaces by means of norm derivatives. It brings together results that have been scattered in various publications over the last two decades and includes more new material and techniques for solving functional equations in normed spaces. Thus the book can serve as an advanced undergraduate or graduate text as well as a resource book for researchers working in geometry of Banach (Hilbert) spaces or in the theory of functional equations (and their applications).Table of ContentsNorm Derivatives; Characterizations of Inner Product Spaces; Orthogonality Relations; Norm Derivatives and Heights; Perpendicular Bisectors in Real Normed Spaces; Bisectrices in Real Normed Spaces; Areas of Triangles in Normed Real Spaces.

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Book SynopsisIn the early 1960s, by using techniques from the model theory of first-order logic, Robinson gave a rigorous formulation and extension of Leibniz' infinitesimal calculus. Since then, the methodology has found applications in a wide spectrum of areas in mathematics, with particular success in the probability theory and functional analysis. In the latter, fruitful results were produced with Luxemburg's invention of the nonstandard hull construction. However, there is still no publication of a coherent and self-contained treatment of functional analysis using methods from nonstandard analysis. This publication aims to fill this gap.Table of ContentsNonstandard Analysis; Banach Spaces; Banach Algerbas; Selected Research Topics.

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Book SynopsisIn the last forty years, nonlinear analysis has been broadly and rapidly developed. Lectures presented in the International Conference on Variational Methods at the Chern Institute of Mathematics in Tianjin of May 2009 reflect this development from different angles. This volume contains articles based on lectures in the following areas of nonlinear analysis: critical point theory, Hamiltonian dynamics, partial differential equations and systems, KAM theory, bifurcation theory, symplectic geometry, geometrical analysis, and celestial mechanics. Combinations of topological, analytical (especially variational), geometrical, and algebraic methods in these researches play important roles. In this proceedings, introductory materials on new theories and surveys on traditional topics are also given. Further perspectives and open problems on hopeful research topics in related areas are described and proposed. Researchers, graduate and postgraduate students from a wide range of areas in mathematics and physics will find contents in this proceedings are helpful.Table of ContentsOn 2-Tori Having a Pole (V Bangert); Turing Patterns and Standing Waves in Fitzhugh-Nagumo Type Systems (C-N Chen & S-Y Kung); Remarks on Mean Value Properties (Y Y Li & L Nguyen); Brake Orbits in Bounded Convex Symmetric Domains (C Liu & D Zhang); Recent Progress on Closed Geodesics in Some Compact Simply Connected Manifolds (Y Long); Topological Bifurcation Theory: Old and New (J Mawhin); Exponential Growth Rate of Paths and Its Connection with Dynamics (Z Xia & P Zhang); Rabinowitz's Theorems Revisited (W Zou); and other papers.

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Book SynopsisThis proceedings is a collection of articles by front-line researchers in Mathematical Analysis, giving the reader a wide perspective of the current research in several areas like Functional Analysis, Complex Analysis and Measure Theory.The works are a fundamental source for current and future developments in these research fields. The articles and surveys have been collected as well as reference results scattered in the corresponding literature and thus, are highly useful to researchers.Table of ContentsWeyl Type Theorems in the Theory of Bounded Linear Operators; Forward Shifts Between Spaces of Continuous Functions; Algebras of Holomorphic Functions; Finitely Additive Measures; Linear Preserver Problems; Diameter Preserving Mappings; The E Property and Many Other Geometric Properties in Banach Spaces.

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Book SynopsisThe asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach — of Estrada, Kanwal and Vindas — is related to moment asymptotic expansions of generalized functions and the Ces'aro behavior. The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. The book can be used by applied mathematicians, physicists, engineers and others who use classical asymptotic methods and wish to consider non-classical objects (generalized functions) and their asymptotics now in a more advanced setting.Table of ContentsAsymptotic Behavior of Generalized Functions: S-Asymptotics F'g; Quasi-Asymptotics in F'; Applications of the Asymptotic Behavior of Generalized Functions: Asymptotic Behavior of Solutions to Partial Differential Equations; Asymptotics and Integral Transforms; Summability of Fourier Series and Integrals.

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Book SynopsisThis book provides a broad introduction to the generalized inverses, Moore-Penrose inverses, Drazin inverses and T-S outer generalized inverses and their perturbation analyses in the spaces of infinite-dimensional. This subject has many applications in operator theory, operator algebras, global analysis and approximation theory and so on.Stable Perturbations of Operators and Related Topics is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students. It is also suitable for researchers as a reference. The proofs of statements and explanations in the book are detailed enough that interested readers can study it by themselves.Table of ContentsWeb Markov Skeleton Processes; Generalised Burgers Equations; Backward Stochastic Differential Equations (BSDEs) Driven by Fractional Brownian Motion; Measure Solutions of BSDEs with Generator of Quadratic Growth; Parameter Estimates of Drift Brownian Motion; Spectral Bounds on Feymann - Kac Semigroups; Stochastic Analysis on Lie Group; Potential Theory of Subordinate Brownian Motion; Stochastic Control of Stochastic Partial Differential Equations with Delay; and other papers.

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Book SynopsisThe theory of hypergroups is a rapidly developing area of mathematics due to its diverse applications in different areas like probability, harmonic analysis, etc. This book exhibits the use of functional equations and spectral synthesis in the theory of hypergroups. It also presents the fruitful consequences of this delicate “marriage” where the methods of spectral analysis and synthesis can provide an efficient tool in characterization problems of function classes on hypergroups.This book is written for the interested reader who has open eyes for both functional equations and hypergroups, and who dares to enter a new world of ideas, a new world of methods — and, sometimes, a new world of unexpected difficulties.Table of ContentsIntroduction; Polynomial Hypergroups in One Variable; Polynomial Hypergroups in Several Variables; Sturm-Liouville Hypergroups; Two-Point Support Hypergroups; Spectral Analysis and Synthesis on Polynomial Hypergroups; Spectral Analysis and Synthesis on Sturm-Liouville Hypergroups; Moment Problems on Hypergroups; Special Functional Equations on Hypergroups; Difference Equations on Polynomial Hypergroups; Stability Problems on Hypergroups.

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Book SynopsisEvolutionary equations are studied in abstract Banach spaces and in spaces of bounded number sequences. For linear and nonlinear difference equations, which are defined on finite-dimensional and infinite-dimensional tori, the problem of reducibility is solved, in particular, in neighborhoods of their invariant sets, and the basics for a theory of invariant tori and bounded semi-invariant manifolds are established. Also considered are the questions on existence and approximate construction of periodic solutions for difference equations in infinite-dimensional spaces and the problem of extendibility of the solutions in degenerate cases. For nonlinear differential equations in spaces of bounded number sequences, new results are obtained in the theory of countable-point boundary-value problems.The book contains new mathematical results that will be useful towards advances in nonlinear mechanics and theoretical physics.Table of ContentsReducibility Problems for Difference Equations; Invariant Tori of Difference Equations in the Space M; Periodic Solutions of Difference Equations, Extention of Solutions; Countable-Point Boundary-Value Problems for Non-Linear Differential Equations in the Space M.

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Book SynopsisThe main goal of the book is to provide a comprehensive and self-contained proof of the, relatively recent, theorem of characterization of the strong maximum principle due to Molina-Meyer and the author, published in Diff. Int. Eqns. in 1994, which was later refined by Amann and the author in a paper published in J. of Diff. Eqns. in 1998. Besides this characterization has been shown to be a pivotal result for the development of the modern theory of spatially heterogeneous nonlinear elliptic and parabolic problems; it has allowed us to update the classical theory on the maximum and minimum principles by providing with some extremely sharp refinements of the classical results of Hopf and Protter-Weinberger. By a celebrated result of Berestycki, Nirenberg and Varadhan, Comm. Pure Appl. Maths. in 1994, the characterization theorem is partially true under no regularity constraints on the support domain for Dirichlet boundary conditions.Instead of encyclopedic generality, this book pays special attention to completeness, clarity and transparency of its exposition so that it can be taught even at an advanced undergraduate level. Adopting this perspective, it is a textbook; however, it is simultaneously a research monograph about the maximum principle, as it brings together for the first time in the form of a book, the most paradigmatic classical results together with a series of recent fundamental results scattered in a number of independent papers by the author of this book and his collaborators.Chapters 3, 4, and 5 can be delivered as a classical undergraduate, or graduate, course in Hilbert space techniques for linear second order elliptic operators, and Chaps. 1 and 2 complete the classical results on the minimum principle covered by the paradigmatic textbook of Protter and Weinberger by incorporating some recent classification theorems of supersolutions by Walter, 1989, and the author, 2003. Consequently, these five chapters can be taught at an undergraduate, or graduate, level. Chapters 6 and 7 study the celebrated theorem of Krein-Rutman and infer from it the characterizations of the strong maximum principle of Molina-Meyer and Amann, in collaboration with the author, which have been incorporated to a textbook by the first time here, as well as the results of Chaps. 8 and 9, polishing some recent joint work of Cano-Casanova with the author. Consequently, the second half of the book consists of a more specialized monograph on the maximum principle and the underlying principal eigenvalues.Table of ContentsThe Minimum Principle; Classifying Supersolutions of Linear Elliptic Problems; The Theorems of Stampacchia and Lax - Milgram; Existence of Weak Solutions; Regularity of Weak Solutions; The Krein - Rutman Theorem; The Strong Maximum Principle; Properties of the Principal Eigenvalue.

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Book SynopsisThis volume provides a systematic survey of almost all the equivalent assertions to the functional equations — zeta symmetry — which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox H-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions.This volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.Table of ContentsIntroduction and Zeta-Functions; G-, H- and Allied Special Functions; The General Modular Relation; The Fourier - Bessel Expansion; The Ewald Expansion; The General Modular Relation for Epstein Zeta-Funcion; The General Modular Relation of Hecke's Type; The General Modular Relation for the Riemann Zeta-Function; The General Modular Relation of ΓΓ-Type; The General Modular Relation of ΓN-Type; The General Modular Relation for Maass Forms.

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Book SynopsisThis is the only book that deals comprehensively with fixed point theorems throughout mathematics. Their importance is due, as the book demonstrates, to their wide applicability. Beyond the first chapter, each of the other seven can be read independently of the others so the reader has much flexibility to follow his/her own interests. The book is written for graduate students and professional mathematicians and could be of interest to physicists, economists and engineers.Table of ContentsEarly Fixed Point Theorems; Fixed Point Theorems in Analysis; The Lefschetz Fixed Point Theorem; Fixed Point Theorems in Geometry; Fixed Points of Volume Preserving Maps; Borel's Fixed Point Theorem in Algebraic Groups; Miscellaneous Fixed Point Theorems; A Fixed Point Theorem in Set Theory.

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Book SynopsisThis book is written for scientists and engineers who use HHT (Hilbert-Huang Transform) to analyze data from nonlinear and non-stationary processes. It can be treated as a HHT user manual and a source of reference for HHT applications. The book contains the basic principle and method of HHT and various application examples, ranging from the correction of satellite orbit drifting to detection of failure of highway bridges.The thirteen chapters of the first edition are based on the presentations made at a mini-symposium at the Society for Industrial and Applied Mathematics in 2003. Some outstanding mathematical research problems regarding HHT development are discussed in the first three chapters. The three new chapters of the second edition reflect the latest HHT development, including ensemble empirical mode decomposition (EEMD) and modified EMD.The book also provides a platform for researchers to develop the HHT method further and to identify more applications.

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Book SynopsisThis book provides an introduction to measure theory and functional analysis suitable for a beginning graduate course, and is based on notes the author had developed over several years of teaching such a course. It is unique in placing special emphasis on the separable setting, which allows for a simultaneously more detailed and more elementary exposition, and for its rapid progression into advanced topics in the spectral theory of families of self-adjoint operators. The author's notion of measurable Hilbert bundles is used to give the spectral theorem a particularly elegant formulation not to be found in other textbooks on the subject.Table of ContentsTopological Spaces; Measure and Integration; Banach Spaces; Dual Banach Spaces; Spectral Theory.

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Book SynopsisThis volume consists of the proofs of 391 problems in Real Analysis: Theory of Measure and Integration (3rd Edition).Most of the problems in Real Analysis are not mere applications of theorems proved in the book but rather extensions of the proven theorems or related theorems. Proving these problems tests the depth of understanding of the theorems in the main text.This volume will be especially helpful to those who read Real Analysis in self-study and have no easy access to an instructor or an advisor.

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Book SynopsisThe theory of Lebesgue and Sobolev spaces with variable integrability is experiencing a steady expansion, and is the subject of much vigorous research by functional analysts, function-space analysts and specialists in nonlinear analysis. These spaces have attracted attention not only because of their intrinsic mathematical importance as natural, interesting examples of non-rearrangement-invariant function spaces but also in view of their applications, which include the mathematical modeling of electrorheological fluids and image restoration.The main focus of this book is to provide a solid functional-analytic background for the study of differential operators on spaces with variable integrability. It includes some novel stability phenomena which the authors have recently discovered.At the present time, this is the only book which focuses systematically on differential operators on spaces with variable integrability. The authors present a concise, natural introduction to the basic material and steadily move toward differential operators on these spaces, leading the reader quickly to current research topics.

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Book SynopsisThis is the first textbook-type presentation of tropical value distribution theory. It provides a detailed introduction of the tropical version of the Nevanlinna theory, describing growth and value distribution analysis of continuous, piecewise linear functions on the real axis. The book also includes applications of this theory to ultra-discrete equations. Three appendices are given to compare the contents of the theory with the classical counterparts in complex analysis.Detailed presentation of the proofs makes the book accessible for lecture courses and independent studies at the graduate and post-doctoral level.Table of ContentsTropical Polynomials, Rationals and Exponentials; Tropical Entire Functions; One-dimensional Tropical Nevanlinna Theory; Clunie and Mohon'ko Type Theorems; Tropical Holomorphic Curves; Representations of Tropical Periodic Functions; Applications to Ultra-Discrete Equations; Appendices: Classical Nevanlinna and Cartan Theories; Introduction to Ultra-Discrete Painleve Equations; Some Operators in Complex Analysis;

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Book SynopsisThis volume contains an important progress on the theory of subnormal operators in the past thirty years, which was developed by the author and his collaborators. It serves as a guide and basis to students and researchers on understanding and exploring further this new direction in operator theory. The volume expounds lucidly on analytic model theory, mosaics, trace formulas of the subnormal operators, and subnormal tuples of operators on the Hilbert spaces.

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Book SynopsisThis book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of pth power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of Hölder and Minkowski. The Lp-spaces thereby emerges in direct analogy with a construction of the real numbers from the rational numbers. This allows grasping the main ideas more rapidly. Other important Banach spaces arising from function spaces and sequence spaces are also treated.In this second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Mapping Theorem, the Closed Graph Theorem and the Hahn-Banach Theorem. The material on operators between normed vector spaces is further expanded in a new Chapter 6, which presents the basic elements of the theory of Fredholm operators on general Banach spaces, not only on Hilbert spaces. This requires that we develop the theory of dual operators between Banach spaces to replace the use of adjoint operators between Hilbert spaces.With the addition of the new material on normed vector spaces and their operators, the book can serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them.Table of ContentsBasic Elements of Metric Topology; New Types of Function Spaces; Theory of Hilbert Spaces; Operators on Hilbert Spaces; Spectral Theory; Fredholm Theory; Exercises;

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Book Synopsis'The book is very well-written by one of the leading figures in the subject. It is self-contained, includes relevant recent advances and is enriched by a large number of examples and illustrations. In addition to the general bibliography, each chapter includes a section of notes, which details the authorship of the main results, and provides useful hints for further readings. Undoubtedly, this edition will be received by researchers with the same success as the first one.'European Mathematical SocietyThis is the standard reference on algebras of Lipschitz functions, written by the leading figure in the field. The second edition includes new chapters on nonlinear Banach space geometry, differentiability in metric measure spaces, and quantum metrics. This latest material reflects the importance of spaces of Lipschitz functions in a diverse range of current research directions. Every functional analyst should have some knowledge of this subject.

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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.

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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

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Book Synopsis

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Book Synopsis

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