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.

●(特價795元)Discrete Fourier Analysis & Wavelets Applications to Signal & Image Precessing

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【簡介】 A thorough guide to the classical and contemporary mathematicalmethods of modern signal and image processing Discrete Fourier Analysis and Wavelets presents athorough introduction to the mathematical foundations of signal andimage processing. Key concepts and applications are addressed in athought-provoking manner and are implemented using vector, matrix,and linear algebra methods. With a balanced focus on mathematicaltheory and computational techniques, this self-contained bookequips readers with the essential knowledge needed to transitionsmoothly from mathematical models to practical digital dataapplications. The book first establishes a complete vector space and matrixframework for analyzing signals and images. Classical methods suchas the discrete Fourier transform, the discrete cosine transform,and their application to JPEG compression are outlined followed bycoverage of the Fourier series and the general theory of innerproduct spaces and orthogonal bases. The book then addressesconvolution, filtering, and windowing techniques for signals andimages. Finally, modern approaches are introduced, includingwavelets and the theory of filter banks as a means of understandingthe multiscale localized analysis underlying the JPEG 2000compression standard. Throughout the book, examples using image compressiondemonstrate how mathematical theory translates into application.Additional applications such as progressive transmission of images,image denoising, spectrographic analysis, and edge detection arediscussed. Each chapter provides a series of exercises as well as aMATLAB project that allows readers to apply mathematical conceptsto solving real problems. Additional MATLAB routines are availablevia the book's related Web site. With its insightful treatment of the underlying mathematics inimage compression and signal processing, Discrete FourierAnalysis and Wavelets is an ideal book formathematics, engineering, and computer science courses at theupper-undergraduate and beginning graduate levels. It is also avaluable resource for mathematicians, engineers, and otherpractitioners who would like to learn more about the relevance ofmathematics in digital data processing. 【目錄】