Principles of Harmonic Analysis

  • Anton Deitmar
  • Siegfried Echterhoff

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Pages 1-32
  3. Pages 33-61
  4. Pages 127-137
  5. Pages 139-158
  6. Pages 159-170
  7. Pages 189-200
  8. Pages 201-231
  9. Pages 233-257
  10. Back Matter
    Pages 259-333

About this book

Introduction

The present book is intended as a text for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up to Anton Deitmer's previous book, A First Course in Harmonic Analysis, or independently, if the students already have a modest knowledge of Fourier Analysis. In this book, among other things, proofs are given of Pontryagin Duality and the Plancherel Theorem for LCA-groups, which were mentioned but not proved in A First Course in Harmonic Analysis. Using Pontryagin duality, the authors also obtain various structure theorems for locally compact abelian groups. The book then proceeds with Harmonic Analysis on non-abelian groups and its applications to theory in number theory and the theory of wavelets.

 

Knowledge of set theoretic topology, Lebesgue integration, and functional analysis on an introductory level will be required in the body of the book. For the convenience of the reader, all necessary ingredients from these areas have been included in the appendices.

 

Professor Deitmar is Professor of Mathematics at the University of Tübingen, Germany. He is a former Heisenberg fellow and has taught in the U.K. for some years. Professor Echterhoff is Professor of Mathematics and Computer Science at the University of Münster, Germany.

Keywords

Abelian group Fourier series Hilbert space algebra boundary element method duality form function functional analysis group harmonic analysis integration theorem topology wavelet

Authors and affiliations

  • Anton Deitmar
    • 1
  • Siegfried Echterhoff
    • 2
  1. 1.Inst. MathematikUniversität TübingenTübingenGermany
  2. 2.Mathematisches InstitutUniversität MünsterMünsterGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-85469-4
  • Copyright Information Springer New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-85468-7
  • Online ISBN 978-0-387-85469-4
  • About this book
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