The Gibbs phenomenon in Fourier analysis, splines and wavelet approximations
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| Format: | Buch |
| Sprache: | English |
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Dordrecht [u.a.]
Kluwer Acad. Publ.
1998
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| Schriftenreihe: | Mathematics and its applications
446 |
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| 100 | 1 | |a Jerri, Abdul J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Gibbs phenomenon in Fourier analysis, splines and wavelet approximations |c by Abdul J. Jerri |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 1998 | |
| 300 | |a XXVII, 336 S. |b graph. Darst. | ||
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| 490 | 1 | |a Mathematics and its applications |v 446 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | THE GIBBS PHENOMENON IN FOURIER ANALYSIS, SPLINES AND WAVELET
APPROXIMATIONS BY ABDUL J. JERRI DEPARTMENT OF MATHEMATICS AND COMPUTER
SCIENCE, CLARKSON UNIVERSITY, POTSDAM, NEW YORK, U.SA. KLUWER ACADEMIC
PUBLISHERS DORDRECHT / BOSTON / LONDON CONTENTS PREFACE XIII
ACKNOWLEDGEMENTS XVII AIM OF THE BOOK XIX 1 INTRODUCTION 1 1.1 THE
GIBBS-WILBRAHAM PHENOMENON 1 1.2 SOME BASIC ELEMENTS OF FOURIER ANALYSIS
. 3 1.3 ILLUSTRATIONS AND ANALYSIS 12 A. THE TRUNCATED FOURIER SERIES
APPROXIMATION 12 B. THE TRUNCATED FOURIER INTEGRAL APPROXIMATION .... 16
1.4 FILTERING VIA THE FEJER AVERAGING 26 A. THE FEJER AVERAGING 28 B.
THE (C, A) SUMMABILITY 31 1.5 THE LANCZOS-LOCAL-TYPE FILTERING 34 2
ANALYSIS AND FILTERING 37 2.1 THE TRUNCATED FOURIER INTEGRAL 38 2.2 THE
FOURIER TRIGONOMETRIC POLYNOMIAL 40 A. A NOTE CONCERNING THE GENERAL
ORTHOGONAL EXPANSION 43 2.3 THE TWO BASIC METHODS OF FILTERING 44 A. THE
LANCZOS-LOCAL-TYPE A- AVERAGING 45 B. THE METHOD OF FEJER AVERAGING AND
SUMMABILITY ... 55 2.4 TRANSFORM METHODS OF FILTERING 56 A. THE
GEGENBAUER TRANSFORM METHOD FOR THE TRUNCATED FOURIER SERIES 57 B. THE
TRUNCATED FOURIER INTEGRALS 67 2.5 EXAMPLES OF OTHER FILTERS 73 THE
FOURIER SERIES IN TWO DIMENSIONS 78 2.6 SOME ADVANTAGES FOR EDGE
DETECTION 80 VN VIII CONTENTS Y 2.7 A HISTORICAL NOTE 83 2.8 _ THE
HIGHER DIMENSIONAL CASE 100 THE GENERAL ORTHOGONAL EXPANSIONS 107 3.1
A BRIEF OVERVIEW 107 3.2 ORTHOGONAL SERIES EXPANSIONS 109 A. THE
STURM-LIOUVILLE PROBLEM 110 B. THE FOURIER-JN-BESSEL SERIES EXPANSION
112 C. THE HANKEL TRANSFORM OF RADIALLY SYMMETRIC FUNC- TIONS IN N
DIMENSIONS 119 D. THE CLASSICAL ORTHOGONAL POLYNOMIALS EXPANSION . . .
122 E. THE LEGENDRE POLYNOMIALS SERIES 122 F. THE TCHEBYCHEV POLYNOMIALS
SERIES 125 G. THE LAGUERRE POLYNOMIALS SERIES 127 H. THE HERMITE
POLYNOMIALS SERIES 130 3.3 THE ASYMPTOTIC RELATION TO FOURIER SERIES 131
RATE OF CONVERGENCE OF THE STURM-LIOUVILLE EIGENFUNC- TIONS EXPANSION
137 SINGULAR STURM-LIOUVILLE PROBLEM 140 3.4 THE GLOBAL EFFECT ON THE
CONVERGENCE IN R N 148 A. THE LAPLACIAN IN N-DIMENSIONAL-FOURIER SERIES
OF RA- DIAL FUNCTIONS 148 B. THE 3-DIMENSIONAL CASE 150 C. THE FOURIER
INTEGRAL REPRESENTATION IN N-DIMENSIONS . 155 3.5 FILTERING FOR
ORTHOGONAL EXPANSIONS 156 A. THE FEJER AVERAGING 156 B. A LANCZOS-LIKE
A-FACTOR FOR GENERAL ORTHOGONAL EX- PANSIONS 157 1. A LANCZOS-LIKE
A-FACTOR FOR FOURIER-J M -BESSEL SERIES . 159 2. ORTHOGONAL POLYNOMIALS
EXPANSIONS 171 3. INTEGRAL TRANSFORMS REPRESENTATIONS 177 I SPLINES AND
OTHER APPROXIMATIONS 183 4.1 THE PIECEWISE-LINEAR APPROXIMATION 184 4.2
HIGH ORDER SPLINES APPROXIMATION 191 4.3 APPROXIMATION IN L P -SENSE 199
4.4 THE INTERPOLATION OF THE DFT 203 » THE WAVELET REPRESENTATIONS 207
5.1 WAVELETS AND FOURIER ANALYSIS 207 A. THE POSSIBLE REASON BEHIND THE
GIBBS PHENOMENON . 207 CONTENTS IX B. ILLUSTRATION OF SOME BASIC
WAVELETS, THEIR FOURIER TRANS- F FORMS AND A GLIMPSE AT THE GIBBS
PHENOMENON . . 216 5.2 ELEMENTS OF WAVELET ANALYSIS 222 A. THE
CONTINUOUS WAVELET (DOUBLE INTEGRAL) REPRESEN- TATION OF FUNCTIONS 222
B. THE DISCRETE WAVELET (DOUBLE) SERIES EXPANSION OF FUNCTIONS 227 5.3
THE DISCRETE WAVELET SERIES APPROXIMATION 230 A. PRELIMINARIES FOR
HAVING DISCRETE ORTHONORMAL WAVELETS231 5.4 THE CONTINUOUS WAVELET
REPRESENTATION 246 A. DETAILED ANALYSIS OF THE GIBBS PHENOMENON FOR EVEN
WAVELETS - THE MEXICAN HAT WAVELET 247 B. THE MEXICAN HAT WAVELET AND
ITS GIBBS PHENOMENON 266 C. HARDY-FUNCTIONS WAVELETS 274 D. RECENT
PRELIMINARY RESULTS 285 REFERENCES 287 APPENDIX A 297 INDEX OF NOTATIONS
319 SUBJECT INDEX V 327 AUTHOR INDEX 335
|
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515/.2435 21 515/.2435 |
| dewey-sort | 3515 42435 221 |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012437923 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T15:02:36Z |
| institution | BVB |
| isbn | 0792351096 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008438948 |
| oclc_num | 39052415 |
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| owner_facet | DE-739 DE-824 DE-91G DE-BY-TUM DE-703 DE-29T DE-521 DE-83 DE-11 |
| physical | XXVII, 336 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spellingShingle | Jerri, Abdul J. The Gibbs phenomenon in Fourier analysis, splines and wavelet approximations Mathematics and its applications Gibbs phenomenon Fourier analysis Spline theory Wavelets (Mathematics) 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 | Gibbs phenomenon Fourier analysis Spline theory Wavelets (Mathematics) Gibbs-Erscheinung (DE-588)4406652-1 gnd |
| topic_facet | Gibbs phenomenon Fourier analysis Spline theory Wavelets (Mathematics) Gibbs-Erscheinung |
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