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Fourier Analysis and Its Applications

  • Anders Vretblad
  • S. Axler
  • F. W. Gehring
  • K. A. Ribet

Part of the Graduate Texts in Mathematics book series (GTM, volume 223)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Anders Vretblad
    Pages 1-13
  3. Anders Vretblad
    Pages 15-37
  4. Anders Vretblad
    Pages 39-72
  5. Anders Vretblad
    Pages 73-103
  6. Anders Vretblad
    Pages 105-135
  7. Anders Vretblad
    Pages 137-163
  8. Anders Vretblad
    Pages 165-195
  9. Anders Vretblad
    Pages 197-226
  10. Anders Vretblad
    Pages 227-237
  11. Back Matter
    Pages 239-269

About this book

Introduction

 This book presents the basic ideas in Fourier analysis and its applications to the study of partial differential equations. It also covers the Laplace and Zeta transformations and the fundaments of their applications. The author has intended to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral or with analytic functions of a complex variable. At the same time, he has included discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually will not find in books at this level.

Many of the chapters end with a summary of their contents, as well as a short historical note. The text contains a great number of examples, as well as more than 350 exercises. In addition, one of the appendices is a collection of the formulas needed to solve problems in the field.

Anders Vretblad is Senior Lecturer of Mathematics at Uppsala University, Sweden.

Keywords

Fourier series Fourier transform calculus differential equation discrete Fourier transform

Authors and affiliations

  • Anders Vretblad
    • 1
  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

Editors and affiliations

  • S. Axler
    • 1
  • F. W. Gehring
    • 2
  • K. A. Ribet
    • 3
  1. 1.Mathematics DepartmentSan Francisco State UniversitySan FranciscoUSA
  2. 2.Mathematics Department East HallUniversity of MichiganAnn ArborUSA
  3. 3.Mathematics DepartmentUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b97452
  • Copyright Information Springer Science+Business Media New York 2003
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-00836-3
  • Online ISBN 978-0-387-21723-9
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site