The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations

A.J. Jerri (Autor)

Buch | Softcover

340 Seiten

2010 | Softcover reprint of hardcover 1st ed. 1998
Springer-Verlag New York Inc.
978-1-4419-4800-7 (ISBN)

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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.

1 Introduction.- 2 Analysis and Filtering.- 3 The General Orthogonal Expansions.- 4 Splines and other Approximations.- 5 The Wavelet Representations.- References.- Appendix A.- Index of Notations.- Author Index.

Erscheint lt. Verlag	19.11.2010
Reihe/Serie	Mathematics and Its Applications ; 446
Zusatzinfo	XXVII, 340 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4419-4800-7 / 1441948007
ISBN-13	978-1-4419-4800-7 / 9781441948007
Zustand	Neuware