The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1998
|
| Schriftenreihe: | Mathematics and Its Applications
446 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book represents the first attempt at a unified picture for the presence 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 addition 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 material 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 involve 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 repetitive 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 |
| Beschreibung: | 1 Online-Ressource (XXVII, 340 p) |
| ISBN: | 9781475728477 9781441948007 |
| DOI: | 10.1007/978-1-4757-2847-7 |
Internformat
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| 500 | |a This book represents the first attempt at a unified picture for the presence 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 addition 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 material 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 involve 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 repetitive 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 | ||
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Datensatz im Suchindex
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| author | Jerri, Abdul J. |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-2847-7 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9781475728477 9781441948007 |
| language | English |
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| spelling | Jerri, Abdul J. Verfasser aut The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations by Abdul J. Jerri Boston, MA Springer US 1998 1 Online-Ressource (XXVII, 340 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 446 This book represents the first attempt at a unified picture for the presence 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 addition 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 material 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 involve 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 repetitive 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 Mathematics Harmonic analysis Fourier analysis Sequences (Mathematics) Computer science / Mathematics Fourier Analysis Computational Mathematics and Numerical Analysis Abstract Harmonic Analysis Sequences, Series, Summability Approximations and Expansions Informatik Mathematik Gibbs-Erscheinung (DE-588)4406652-1 gnd rswk-swf Gibbs-Erscheinung (DE-588)4406652-1 s 1\p DE-604 Mathematics and Its Applications 446 (DE-604)BV008163334 446 https://doi.org/10.1007/978-1-4757-2847-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jerri, Abdul J. The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations Mathematics and Its Applications Mathematics Harmonic analysis Fourier analysis Sequences (Mathematics) Computer science / Mathematics Fourier Analysis Computational Mathematics and Numerical Analysis Abstract Harmonic Analysis Sequences, Series, Summability Approximations and Expansions Informatik Mathematik Gibbs-Erscheinung (DE-588)4406652-1 gnd |
| subject_GND | (DE-588)4406652-1 |
| title | The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations |
| title_auth | The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations |
| title_exact_search | The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations |
| title_full | The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations by Abdul J. Jerri |
| title_fullStr | The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations by Abdul J. Jerri |
| title_full_unstemmed | The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations by Abdul J. Jerri |
| title_short | The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations |
| title_sort | the gibbs phenomenon in fourier analysis splines and wavelet approximations |
| topic | Mathematics Harmonic analysis Fourier analysis Sequences (Mathematics) Computer science / Mathematics Fourier Analysis Computational Mathematics and Numerical Analysis Abstract Harmonic Analysis Sequences, Series, Summability Approximations and Expansions Informatik Mathematik Gibbs-Erscheinung (DE-588)4406652-1 gnd |
| topic_facet | Mathematics Harmonic analysis Fourier analysis Sequences (Mathematics) Computer science / Mathematics Fourier Analysis Computational Mathematics and Numerical Analysis Abstract Harmonic Analysis Sequences, Series, Summability Approximations and Expansions Informatik Mathematik Gibbs-Erscheinung |
| url | https://doi.org/10.1007/978-1-4757-2847-7 |
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