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© 2002

A First Course in Harmonic Analysis

  • direct and streamlined approach to central concepts

Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Fourier Analysis

    1. Front Matter
      Pages 1-1
    2. Anton Deitmar
      Pages 3-20
    3. Anton Deitmar
      Pages 21-36
    4. Anton Deitmar
      Pages 37-53
  3. LCA Groups

    1. Front Matter
      Pages 55-55
    2. Anton Deitmar
      Pages 57-63
    3. Anton Deitmar
      Pages 65-78
    4. Anton Deitmar
      Pages 79-87
    5. Anton Deitmar
      Pages 89-104
  4. Noncommutative Groups

    1. Front Matter
      Pages 105-105
    2. Anton Deitmar
      Pages 107-118
    3. Anton Deitmar
      Pages 119-125
    4. Anton Deitmar
      Pages 127-134
  5. Back Matter
    Pages 135-152

About this book

Introduction

This book is a primer in harmonic analysis on the undergraduate level. It gives a lean and streamlined introduction to the central concepts of this beautiful and utile theory. In contrast to other books on the topic, A First Course in Harmonic Analysis is entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topology. Nevertheless, almost all proofs are given in full and all central concepts are presented clearly.
The first aim of this book is to provide an introduction to Fourier analysis, leading up to the Poisson Summation Formula. The second aim is to make the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The third goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.
The reader interested in the central concepts and results of harmonic analysis will benefit from the streamlined and direct approach of this book.
Professor Deitmar holds a Chair in Pure Mathematics at the University of Exeter, U.K. He is a former Heisenberg fellow and was awarded the main prize of the Japanese Association of Mathematical Sciences in 1998. In his leisure time he enjoys hiking in the mountains and practising Aikido.

Keywords

Fourier analysis Fourier series Riemann integral harmonic analysis integral integration metric space

Authors and affiliations

  1. 1.Department of MathematicsUniversity of ExeterExeter, DevonUK

Bibliographic information

  • Book Title A First Course in Harmonic Analysis
  • Authors Anton Deitmar
  • Series Title Universitext
  • DOI https://doi.org/10.1007/978-1-4757-3834-6
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-95375-5
  • Softcover ISBN 978-1-4757-3836-0
  • eBook ISBN 978-1-4757-3834-6
  • Series ISSN 0172-5939
  • Series E-ISSN 2191-6675
  • Edition Number 1
  • Number of Pages XI, 152
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Topological Groups, Lie Groups
    Analysis
  • Buy this book on publisher's site

Reviews

From the reviews of the first edition:

A. Deitmar

A First Course in Harmonic Analysis

"An excellent introduction to the basic concepts of this beautiful theory, without too much technical overload . . . In this well-written textbook the central concepts of Harmonic Analysis are explained in an enjoyable way, while using very little technical background. Quite surprisingly this approach works. It is not an exaggeration that each undergraduate student interested in and each professor teaching Harmonic Analysis will benefits from the streamlined and direct approach of this book."—ACTA SCIENTIARUM MATHEMATICARUM

"This is a well thought thorough introduction to harmonic analysis … efficient, swift, elegant and concentrated. … It makes for an excellent text book, an instructor’s delight and a pleasure for students because of the precise formulation and the concise proofs in a little over one hundred pages. … A gem of a first course in harmonic analysis, heartily recommended." (A. Dijksma, Nieuw Archief voor Wiskunde, Vol. 7 (3), 2006)