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Fourier Analysis on Finite Abelian Groups

  • Authors
  • Bao Luong

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages 1-14
  2. Bao Luong
    Pages 1-22
  3. Bao Luong
    Pages 23-32
  4. Bao Luong
    Pages 33-47
  5. Bao Luong
    Pages 49-66
  6. Bao Luong
    Pages 81-91
  7. Bao Luong
    Pages 131-139
  8. Bao Luong
    Pages 141-151
  9. Back Matter
    Pages 1-5

About this book

Introduction

Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, cryptography, algorithms, and sequence design. This self-contained book provides a thorough look at the Fourier transform, one of the most useful tools in applied mathematics.

With countless examples and unique exercise sets at the end of most sections, Fourier Analysis on Finite Abelian Groups is a perfect companion for a first course in Fourier analysis. The first two chapters provide fundamental material for a strong foundation to deal with subsequent chapters.

Special topics covered include:

* Computing eigenvalues of the Fourier transform

* Applications to Banach algebras

* Tensor decompositions of the Fourier transform

* Quadratic Gaussian sums

This book provides a useful introduction for well-prepared undergraduate and graduate students and powerful applications that may appeal to researchers and mathematicians. The only prerequisites are courses in group theory and linear algebra.

Keywords

Banach algebras Chebyshev systems Fourier transform Gaussian sums algebra finite abelian groups quadratic Gaussian sums tensor decomposition vector spaces

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4916-6
  • Copyright Information Birkhäuser Boston 2009
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4915-9
  • Online ISBN 978-0-8176-4916-6
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • Buy this book on publisher's site