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＜電子ブック＞
The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations / by A.J. Jerri
(Mathematics and Its Applications ; 446)

版	1st ed. 1998.
出版者	(New York, NY : Springer US : Imprint: Springer)
出版年	1998
本文言語	英語
大きさ	XXVII, 340 p : online resource
著者標目	*Jerri, A.J author SpringerLink (Online service)
件　名	LCSH:Fourier analysis LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Harmonic analysis LCSH:Sequences (Mathematics) LCSH:Approximation theory FREE:Fourier Analysis FREE:Computational Mathematics and Numerical Analysis FREE:Abstract Harmonic Analysis FREE:Sequences, Series, Summability FREE:Approximations and Expansions
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4757-2847-7

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