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The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations

  • Book
  • © 1998

Overview

Authors:
  1. Abdul J. Jerri

    1. Department of Mathematics and Computer Science, Clarkson University, Potsdam, USA

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xxvii
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  2. Introduction

    • Abdul J. Jerri
    Pages 1-36

  3. Analysis and Filtering

    • Abdul J. Jerri
    Pages 37-105

  4. The General Orthogonal Expansions

    • Abdul J. Jerri
    Pages 107-181

  5. Splines and other Approximations

    • Abdul J. Jerri
    Pages 183-205

  6. The Wavelet Representations

    • Abdul J. Jerri
    Pages 207-286

  7. Back Matter

    Pages 287-340
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics and Computer Science, Clarkson University, Potsdam, USA

    Abdul J. Jerri

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