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© 2003

Fourier Analysis and Its Applications

  • S. Axler
  • F. W. Gehring
  • K. A. Ribet
Textbook

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

  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

About the editors

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

Bibliographic information

  • Book Title Fourier Analysis and Its Applications
  • Authors Anders Vretblad
  • Series Title Graduate Texts in Mathematics
  • 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
  • Hardcover ISBN 978-0-387-00836-3
  • Softcover ISBN 978-1-4419-1841-3
  • eBook ISBN 978-0-387-21723-9
  • Series ISSN 0072-5285
  • Series E-ISSN 2197-5612
  • Edition Number 1
  • Number of Pages XII, 272
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Fourier Analysis
  • Buy this book on publisher's site

Reviews

From the reviews:

"This book is one in the Graduate Texts in Mathematics series published by Springer. … There is a variety of worked examples as well as 350-plus exercises … . The book is a valuable addition to the literature on Fourier analysis. It is written with more mathematical rigour than many texts … without being totally opaque to the non-specialist. … The examples at the end of each chapter are well structured and a reader working through most of them will achieve a good understanding of the topics." (Graham Brindley, The Mathematical Gazette, Vol. 90 (517), 2006)

"The author … presents the results of his experiences and choices for decades of teaching courses. … The tables and formulas collected … are of great service. At the end of each chapter there is a summary section that discusses the results, gives some history, and suggests instructive exercises. We thus have a solid course on Fourier analysis and its applications interesting for students and specialists in engineering as well as for mathematicians. … I believe that the book will find numerous interested readers." (Elijah Liflyand, Zentralblatt MATH, Vol. 1032 (7), 2004)

"This book is an interesting mixture of a traditional approach … and a more modern one, emphasizing the role of (tempered) distributions and the application aspects of Fourier analysis. … The book is certainly highly recommendable for those who want to learn the essence of Fourier analysis in a mathematically correct way without having to go through too much technical details." (H.G. Feichtinger, Monatshefte für Mathematik, Vol. 143 (2), 2004)

"The book is appropriate for an advanced undergraduate or a master’s level one-term introductory course on Fourier series with applications to boundary value problems. … a deep idea is presented in a non-rigorous way both to show the usefulness of the idea and to stimulate interest in further study. … The book has a good collection of exercises … . Each chapter ends with both a summary of its main results and methods and historical notes." (Colin C. Graham, Mathematical Reviews, Issue 2004 e)