Mathematics and Its Applications

The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations

Authors: Jerri, A.J.

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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.

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $169.00
price for USA in USD
  • ISBN 978-1-4757-2847-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Hardcover $219.99
price for USA in USD
Softcover $219.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations
Authors
Series Title
Mathematics and Its Applications
Series Volume
446
Copyright
1998
Publisher
Springer US
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-1-4757-2847-7
DOI
10.1007/978-1-4757-2847-7
Hardcover ISBN
978-0-7923-5109-2
Softcover ISBN
978-1-4419-4800-7
Edition Number
1
Number of Pages
XXVII, 340
Topics