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A First Course in Harmonic Analysis

  • Textbook
  • © 2002

Overview

Authors:
  1. Anton Deitmar

    1. Department of Mathematics, University of Exeter, Exeter, Devon, UK

  • direct and streamlined approach to central concepts

Part of the book series: Universitext (UTX)

  • 13k Accesses

  • 34 Citations

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About this book

This book is intended as a primer in harmonic analysis at the un­ dergraduate level. All the central concepts of harmonic analysis are introduced without too much technical overload. For example, the book is based entirely on the Riemann integral instead of the more demanding Lebesgue integral. Furthermore, all topological questions are dealt with purely in the context of metric spaces. It is quite sur­ prising that this works. Indeed, it turns out that the central concepts theory can be explained using very little of this beautiful and useful technical background. The first aim of this book is to give a lean introduction to Fourier analysis, leading up to the Poisson summation formula. The sec­ ond 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.

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Fourier Analysis

    1. Front Matter

      Pages 1-1
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    2. Fourier Series

      • Anton Deitmar
      Pages 3-20

    3. Hilbert Spaces

      • Anton Deitmar
      Pages 21-36

    4. The Fourier Transform

      • Anton Deitmar
      Pages 37-53

  3. LCA Groups

    1. Front Matter

      Pages 55-55
      Download chapter PDF

    2. Finite Abelian Groups

      • Anton Deitmar
      Pages 57-63

    3. LCA Groups

      • Anton Deitmar
      Pages 65-78

    4. The Dual Group

      • Anton Deitmar
      Pages 79-87

    5. Plancherel Theorem

      • Anton Deitmar
      Pages 89-104

  4. Noncommutative Groups

    1. Front Matter

      Pages 105-105
      Download chapter PDF

    2. Matrix Groups

      • Anton Deitmar
      Pages 107-118

    3. The Representations of SU(2)

      • Anton Deitmar
      Pages 119-125

    4. The Peter-Weyl Theorem

      • Anton Deitmar
      Pages 127-134

  5. Back Matter

    Pages 135-152
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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)

Authors and Affiliations

  • Department of Mathematics, University of Exeter, Exeter, Devon, UK

    Anton Deitmar

Accessibility Information

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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

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2002

  • eBook ISBN: 978-1-4757-3834-6Published: 17 April 2013

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XI, 152

  • Topics: Topological Groups, Lie Groups, Analysis

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