Applied and Numerical Harmonic Analysis

A Basis Theory Primer

Expanded Edition

Authors: Heil, Christopher

  • Unique book in the literature
  • A clear and accessible text with detailed explanations of abstract material
  • Suitable for classroom use or independent study
  • Covers abstract material with a high degree of relevance to a wide variety of modern topics
  • Written for a broad audience of graduate students, pure and applied mathematicians as well as engineers
  • Includes extensive exercises at the end of each section
  • Separate solutions manual available for instructors upon request
see more benefits

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price for USA (gross)
  • ISBN 978-0-8176-4687-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Hardcover $84.95
price for USA
  • ISBN 978-0-8176-4686-8
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  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
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About this Textbook

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.

Reviews

From the reviews:

“The present book gives a wide perspective, preparing the functional analytic ground … and also discussing in great detail the relevant features of bases in Banach spaces, unconditional bases, frames, and their role in the context of Applied Harmonic Analysis. … the book is ideally suited for self-study, but also as a text book from which different courses can be compiled. The presentation is very reader-friendly and provides all necessary details.” (H. G. Feichtinger, Monatshefte für Mathematik, Vol. 166 (3-4), June, 2012)

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. … The exercises contained in the book make it a good fit for graduate courses on selected topics in functional analysis and applications.” (Bernhard Bodmann, Zentralblatt MATH, Vol. 1227, 2012)

“The amount of mathematics treated in the book is impressive. … a handbook for a certain group of mathematicians to learn about the main tools of the theory of bases and frames for Banach and Hilbert spaces. … Personally I like this book. It is one of those very few mathematical books that I can read without additional difficulties arising from my limited capacity to remember facts and definitions.” (Kazaros Kazarian, Mathematical Reviews, Issue 2012 b)


Table of contents (16 chapters)

  • Banach Spaces and Operator Theory

    Heil, Christopher

    Pages 3-55

  • Functional Analysis

    Heil, Christopher

    Pages 57-83

  • Unconditional Convergence of Series in Banach and Hilbert Spaces

    Heil, Christopher

    Pages 87-123

  • Bases in Banach Spaces

    Heil, Christopher

    Pages 125-151

  • Biorthogonality, Minimality, and More About Bases

    Heil, Christopher

    Pages 153-176

Buy this book

eBook $64.99
price for USA (gross)
  • ISBN 978-0-8176-4687-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $84.95
price for USA
  • ISBN 978-0-8176-4686-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
A Basis Theory Primer
Book Subtitle
Expanded Edition
Authors
Series Title
Applied and Numerical Harmonic Analysis
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-8176-4687-5
DOI
10.1007/978-0-8176-4687-5
Hardcover ISBN
978-0-8176-4686-8
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XXV, 537
Number of Illustrations and Tables
42 b/w illustrations
Topics