The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations

  • Abdul J. Jerri

Part of the Mathematics and Its Applications book series (MAIA, volume 446)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Abdul J. Jerri
    Pages 1-36
  3. Abdul J. Jerri
    Pages 37-105
  4. Abdul J. Jerri
    Pages 107-181
  5. Abdul J. Jerri
    Pages 183-205
  6. Abdul J. Jerri
    Pages 207-286
  7. Back Matter
    Pages 287-340

About this book

Introduction

This book represents the first attempt at a unified picture for the pres­ ence of the Gibbs (or Gibbs-Wilbraham) phenomenon in applications, its analysis and the different methods of filtering it out. The analysis and filtering cover the familiar Gibbs phenomenon in Fourier series and integral representations of functions with jump discontinuities. In ad­ dition it will include other representations, such as general orthogonal series expansions, general integral transforms, splines approximation, and continuous as well as discrete wavelet approximations. The mate­ rial in this book is presented in a manner accessible to upperclassmen and graduate students in science and engineering, as well as researchers who may face the Gibbs phenomenon in the varied applications that in­ volve the Fourier and the other approximations of functions with jump discontinuities. Those with more advanced backgrounds in analysis will find basic material, results, and motivations from which they can begin to develop deeper and more general results. We must emphasize that the aim of this book (the first on the sUbject): to satisfy such a diverse audience, is quite difficult. In particular, our detailed derivations and their illustrations for an introductory book may very well sound repeti­ tive to the experts in the field who are expecting a research monograph. To answer the concern of the researchers, we can only hope that this book will prove helpful as a basic reference for their research papers.

Keywords

Approximation calculus fourier analysis integral transform wavelet

Authors and affiliations

  • Abdul J. Jerri
    • 1
  1. 1.Department of Mathematics and Computer ScienceClarkson UniversityPotsdamUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2847-7
  • Copyright Information Springer-Verlag US 1998
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-4800-7
  • Online ISBN 978-1-4757-2847-7
  • About this book