Overview

The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications. No other text develops the ties between classical basis theory and its modern uses in applied harmonic analysis.

Full Product Details

Author:   Christopher Heil
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   Enlarged edition
Dimensions:   Width: 15.50cm , Height: 3.10cm , Length: 23.50cm
Weight:   2.120kg
ISBN:  

9780817646868

ISBN 10:   0817646868
Pages:   537
Publication Date:   11 November 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Language:   English

Table of Contents

ANHA Series Preface.- Preface.- General Notation.- Part I. A Primer on Functional Analysis .- Banach Spaces and Operator Theory.- Functional Analysis.- Part II. Bases and Frames.- Unconditional Convergence of Series in Banach and Hilbert Spaces.- Bases in Banach Spaces.- Biorthogonality, Minimality, and More About Bases.- Unconditional Bases in Banach Spaces.- Bessel Sequences and Bases in Hilbert Spaces.- Frames in Hilbert Spaces.- Part III. Bases and Frames in Applied Harmonic Analysis.- The Fourier Transform on the Real Line.- Sampling, Weighted Exponentials, and Translations.- Gabor Bases and Frames.- Wavelet Bases and Frames.- Part IV. Fourier Series.- Fourier Series.- Basic Properties of Fourier Series.- Part V. Appendices.- Lebesgue Measure and Integration.- Compact and Hilbert–Schmidt Operators.- Hints for Exercises.- Index of Symbols.- References.- Index.

Reviews

This book is a very comprehensive work dedicated to introducing graduate students or researchers in pure and applied mathematics as well as engineering to the foundations of basis expansions and to essential techniques for applications. ... Chris Heil's book explains many aspects of Fourier's legacy which go beyond harmonic analysis, including Banach space geometry, nonharmonic Fourier analysis, and the modern theory of frames. The exercises contained in the book make it a good fit for graduate courses on selected topics in functional analysis and applications. ... [T]he book completes a tour from the fundamentals of functional analysis to currently active research related to basis expansions. ... Many topics in Chris Heil's book are also covered [elsewhere] but the level of detail found here is greater. --ZentralBlatt MATH

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