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A Basis Theory Primer: Expanded Edition (Applied and Numerical Harmonic Analysis)

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A Basis Theory Primer: Expanded Edition (Applied and Numerical Harmonic Analysis) Cover

 

Synopses & Reviews

Publisher Comments:

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 its 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. * Part I develops the functional analysis that underlies most of the concepts presented in the later parts of the text. * Part II presents the abstract theory of bases and frames in Banach and Hilbert spaces, including the classical topics of convergence, Schauder bases, biorthogonal systems, and unconditional bases, followed by the more recent topics of Riesz bases and frames in Hilbert spaces. * Part III relates bases and frames to applied harmonic analysis, including sampling theory, Gabor analysis, and wavelet theory. * Part IV deals with classical harmonic analysis and Fourier series, emphasizing the role played by bases, which is a different viewpoint from that taken in most discussions of Fourier series. Key features: * Self-contained presentation with clear proofs accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications. * Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses; hints for selected exercises are included at the end of the book. * A separate solutions manual is available for instructors upon request at: www.birkhauser-science.com/978-0-8176-4686-8/. * No other text develops the ties between classical basis theory and its modern uses in applied harmonic analysis. A Basis Theory Primer is suitable for independent study or as the basis for a graduate-level course. Instructors have several options for building a course around the text depending on the level and background of their students.

Synopsis:

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.

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.

Product Details

ISBN:
9780817646868
Author:
Heil, Christopher
Publisher:
Birkhauser
Location:
Boston, MA
Subject:
Mathematical Analysis
Subject:
Banach spaces
Subject:
Hilbert spaces.
Subject:
Bases
Subject:
Convergence
Subject:
Frames
Subject:
Functional Analysis
Subject:
infinite series
Subject:
abstract harmonic analysis
Subject:
Appl.Mathematics/Computational Methods of Engineering
Subject:
Fourier analysis
Subject:
APPLICATIONS OF MATHEMATICS
Subject:
Signal, Image and Speech Processing
Subject:
Mathematics-Analysis General
Subject:
Mathematics
Subject:
The Arts
Subject:
mathematics and statistics
Subject:
Harmonic analysis
Subject:
Engineering mathematics
Copyright:
Edition Description:
2011
Series:
Applied and Numerical Harmonic Analysis
Publication Date:
20101111
Binding:
HARDCOVER
Language:
English
Pages:
562
Dimensions:
235 x 155 mm 2120 gr

Related Subjects

Engineering » Engineering » General Engineering
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Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Harmonic Analysis

A Basis Theory Primer: Expanded Edition (Applied and Numerical Harmonic Analysis) New Hardcover
0 stars - 0 reviews
$84.95 In Stock
Product details 562 pages Springer - English 9780817646868 Reviews:
"Synopsis" by , 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.
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