Analysis in Banach Spaces: Volume III: Harmonic Analysis and Spectral Theory

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This third volume of Analysis in Banach Spaces offers a systematic treatment of Banach space-valued singular integrals, Fourier transforms, and function spaces. It further develops and ramifies the theory of functional calculus from Volume II and describes applications of these new notions and tools to the problem of maximal regularity of evolution equations. The exposition provides a unified treatment of a large body of results, much of which has previously only been available in the form of research papers. Some of the more classical topics are presented in a novel way using modern techniques amenable to a vector-valued treatment. Thanks to its accessible style with complete and detailed proofs, this book will be an invaluable reference for researchers interested in functional analysis, harmonic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.

Problems and Solutions in Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions and Quantum Mechanics

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This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions. The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Normed Spaces and Banach Spaces Contents: Normed Spaces and Banach Spaces Hilbert Spaces Finite Dimensional Hilbert Spaces Hilbert Space L₂(Ω) Hilbert Space ℓ₂(II) Fourier Transform Wavelets Holomorphic Entire Functions and Hilbert Space Generalized Functions Quantum Mechanics Readership: Advanced undergraduate, graduate and post-graduate students in mathematics and theoretical physics. The book is also suitable for those taking courses in functional analysis and quantum theory.