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Principles of Harmonic Analysis

  • Anton Deitmar
  • Siegfried Echterhoff

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Anton Deitmar, Siegfried Echterhoff
    Pages 1-35
  3. Anton Deitmar, Siegfried Echterhoff
    Pages 37-60
  4. Anton Deitmar, Siegfried Echterhoff
    Pages 61-83
  5. Anton Deitmar, Siegfried Echterhoff
    Pages 85-106
  6. Anton Deitmar, Siegfried Echterhoff
    Pages 107-121
  7. Anton Deitmar, Siegfried Echterhoff
    Pages 123-131
  8. Anton Deitmar, Siegfried Echterhoff
    Pages 133-151
  9. Anton Deitmar, Siegfried Echterhoff
    Pages 153-163
  10. Anton Deitmar, Siegfried Echterhoff
    Pages 165-183
  11. Anton Deitmar, Siegfried Echterhoff
    Pages 185-194
  12. Anton Deitmar, Siegfried Echterhoff
    Pages 195-223
  13. Anton Deitmar, Siegfried Echterhoff
    Pages 225-245
  14. Anton Deitmar, Siegfried Echterhoff
    Pages 247-267
  15. Back Matter
    Pages 269-332

About this book

Introduction

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.

Keywords

Abelian Groups Direct and Indirect Integrals Fourier Analysis Harmonic Analysis Pontryagin Duality Selberg Trace Formula

Authors and affiliations

  • Anton Deitmar
    • 1
  • Siegfried Echterhoff
    • 2
  1. 1.Universität Tübingen Inst. MathematikTübingenGermany
  2. 2.Universität Münster Mathematisches InstitutMünsterGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-05792-7
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-05791-0
  • Online ISBN 978-3-319-05792-7
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site