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Principles of Harmonic Analysis

  • Textbook
  • © 2014

Overview

Authors:
  1. Anton Deitmar

    1. Universität Tübingen Inst. Mathematik, Tübingen, Germany

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    You can also search for this author in PubMed   Google Scholar

  2. Siegfried Echterhoff

    1. Universität Münster Mathematisches Institut, Münster, Germany

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    You can also search for this author in PubMed   Google Scholar

  • Second edition is completely revised and updated, including many new exercises and theorems
  • New chapter on p-adic and abelic groups
  • Updated appendices on theoretic topology, Lebesgue integration, and functional analysis
  • Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Haar Integration

    • Anton Deitmar, Siegfried Echterhoff
    Pages 1-35

  3. Banach Algebras

    • Anton Deitmar, Siegfried Echterhoff
    Pages 37-60

  4. Duality for Abelian Groups

    • Anton Deitmar, Siegfried Echterhoff
    Pages 61-83

  5. The Structure of LCA-Groups

    • Anton Deitmar, Siegfried Echterhoff
    Pages 85-106

  6. Operators on Hilbert Spaces

    • Anton Deitmar, Siegfried Echterhoff
    Pages 107-121

  7. Representations

    • Anton Deitmar, Siegfried Echterhoff
    Pages 123-131

  8. Compact Groups

    • Anton Deitmar, Siegfried Echterhoff
    Pages 133-151

  9. Direct Integrals

    • Anton Deitmar, Siegfried Echterhoff
    Pages 153-163

  10. The Selberg Trace Formula

    • Anton Deitmar, Siegfried Echterhoff
    Pages 165-183

  11. The Heisenberg Group

    • Anton Deitmar, Siegfried Echterhoff
    Pages 185-194

  12. \({\rm SL}_2({\mathbb R})\)

    • Anton Deitmar, Siegfried Echterhoff
    Pages 195-223

  13. Wavelets

    • Anton Deitmar, Siegfried Echterhoff
    Pages 225-245

  14. p-Adic Numbers and Adeles

    • Anton Deitmar, Siegfried Echterhoff
    Pages 247-267

  15. Back Matter

    Pages 269-332
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Keywords

About this book

This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.

Authors and Affiliations

  • Universität Tübingen Inst. Mathematik, Tübingen, Germany

    Anton Deitmar

  • Universität Münster Mathematisches Institut, Münster, Germany

    Siegfried Echterhoff

About the authors

Anton Deitmar is a professor of Mathematics at the University of Tübingen, Germany. Siegfried Echterhoff is a professor of Mathematics at the University of Münster, Germany.

Bibliographic Information

  • Book Title: Principles of Harmonic Analysis

  • Authors: Anton Deitmar, Siegfried Echterhoff

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-319-05792-7

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2014

  • Hardcover ISBN: 978-3-319-05791-0Published: 07 July 2014

  • Softcover ISBN: 978-3-319-37904-3Published: 17 September 2016

  • eBook ISBN: 978-3-319-05792-7Published: 21 June 2014

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 2

  • Number of Pages: XIII, 332

  • Number of Illustrations: 11 b/w illustrations

  • Topics: Abstract Harmonic Analysis, Visualization, Applications of Mathematics

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