Wavelets and other orthogonal systems with applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton u.a.
CRC Press
1994
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 248 S. |
| ISBN: | 0849378788 |
Internformat
MARC
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| 100 | 1 | |a Walter, Gilbert G. |d 1930- |e Verfasser |0 (DE-588)121517926 |4 aut | |
| 245 | 1 | 0 | |a Wavelets and other orthogonal systems with applications |c Gilbert G. Walter |
| 264 | 1 | |a Boca Raton u.a. |b CRC Press |c 1994 | |
| 300 | |a X, 248 S. | ||
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Datensatz im Suchindex
| _version_ | 1804124417204158464 |
|---|---|
| adam_text | Table of Contents
Preface m
1 Orthogonal Series 1
1.1 General theory 1
1.2 Examples 5
1.2.1 Trigonometric system 5
1.2.2 Haar system 9
1.2.3 Shannon system 10
1.3 Problems 13
2 A Primer on Tempered
Distributions 15
2.1 Tempered distributions 16
2.2 Fourier transforms 21
2.3 Periodic distributions 23
2.4 Analytic representations 24
2.5 Sobolev spaces 26
2.6 Problems 26
3 An Introduction to Orthogonal
Wavelet Theory 28
3.1 Multiresolution analysis 29
3.2 Mother wavelet 33
3.3 Reproducing kernels and a moment condition 38
3.4 Regularity of wavelets as a moment condition 39
3.5 Mallat s decomposition and reconstruction algorithm 43
3.6 Filters 45
3.7 Problems 48
viii Table of Contents
4 Convergence and Summability
of Fourier Series 50
4.1 Pointwise convergence 50
4.2 Summability 55
4.3 Gibbs phenomenon 56
4.4 Periodic distributions 58
4.5 Problems 60
5 Wavelets and Tempered
Distributions 63
5.1 Multiresolution analysis of tempered distributions 64
5.2 Wavelets based on distributions 67
5.2.1 Distribution solutions of dilation equations 67
5.2.2 A partial distributional multiresolution
analysis 70
5.3 Distributions with point support 71
5.4 Problems 75
6 Orthogonal Polynomials 76
6.1 General theory 76
6.2 Classical orthogonal polynomials 81
6.2.1 Legendre polynomials 81
6.2.2 Jacobi polynomials 85
6.2.3 Laguerre polynomials 85
6.2.4 Hermite polynomials 86
6.3 Problems 91
7 Other Orthogonal Systems 93
7.1 Self adjoint eigenvalue problems on a finite interval 93
7.2 Hilbert Schmidt integral operators 96
7.3 An anomaly—the prolate spheroidal functions 97
7.4 A lucky accident? 99
7.5 Rademacher functions 103
7.6 Walsh functions 104
7.7 Periodic wavelets 105
7.8 Local sine or cosine bases 107
7.9 Biorthogonal wavelets 111
7.10 Problems 114
Table of Contents ix
8 Pointwise Convergence of Wavelet
Expansions ii6
8.1 Quasi positive delta sequences 117
8.2 Local convergence of distribution expansions 120
8.3 Convergence almost everywhere 124
8.4 Rate of convergence of the delta sequence 124
8.5 Other partial sums of the wavelet expansion 128
8.6 Gibbs phenomenon 130
8.7 Problems 132
9 A Shannon Sampling Theorem
in Vm 134
9.1 A Riesz basis of Vm 135
9.2 The sampling sequence in Vm 136
9.3 Examples of sampling theorems 138
9.4 The sampling sequence in Tm 140
9.5 Shifted sampling 143
9.6 Oversampling with scaling functions 145
9.7 Cardinal scaling functions 149
9.8 Problems 156
10 Translation and Dilation Invari
ance in Orthogonal Systems 158
10.1 Trigonometric system 158
10.2 Orthogonal polynomials 159
10.3 An example where everything works 160
10.4 An example where nothing works 161
10.5 Weak translation invariance 161
10.6 Dilations and other operations 167
10.7 Problems 168
11 Analytic Representations Via
Orthogonal Series 170
11.1 Trigonometric series 170
11.2 Hermite series 174
11.3 Legendre polynomial series 179
11.4 Analytic and harmonic wavelets 180
11.5 Analytic solutions to dilation equations 183
11.6 Analytic representation of distributions by wavelets 184
11.7 Problems 188
x Table of Contents
12 Orthogonal Series in Statistics 190
12.1 Fourier series density estimators 191
12.2 Hermite series density estimators 194
12.3 The histogram as a wavelet estimator 195
12.4 Smooth wavelet estimators of density 199
12.5 Local convergence 203
12.6 Positive density estimators 204
12.7 Other estimation with wavelets 205
12.7.1 Mixture problems 206
12.7.2 Spectral density estimation 211
12.7.3 Regression estimators 212
12.8 Problems 213
13 Orthogonal Systems and
Stochastic Processes 215
13.1 K L expansions 215
13.2 Stationary processes and wavelets 218
13.3 A series with uncorrelated coefficients 220
13.4 Wavelets based on band limited processes 226
13.5 Nonstationary processes 229
13.6 Problems 231
Bibliography 233
Index 24i
|
| any_adam_object | 1 |
| author | Walter, Gilbert G. 1930- |
| author_GND | (DE-588)121517926 |
| author_facet | Walter, Gilbert G. 1930- |
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| author_sort | Walter, Gilbert G. 1930- |
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| ctrlnum | (OCoLC)832176569 (DE-599)BVBBV010035593 |
| dewey-full | 515.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.2433 |
| dewey-search | 515.2433 |
| dewey-sort | 3515.2433 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV010035593 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:45:20Z |
| institution | BVB |
| isbn | 0849378788 |
| language | English |
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| physical | X, 248 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Walter, Gilbert G. 1930- Verfasser (DE-588)121517926 aut Wavelets and other orthogonal systems with applications Gilbert G. Walter Boca Raton u.a. CRC Press 1994 X, 248 S. txt rdacontent n rdamedia nc rdacarrier Wavelet (DE-588)4215427-3 gnd rswk-swf Wavelet (DE-588)4215427-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006655056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Walter, Gilbert G. 1930- Wavelets and other orthogonal systems with applications Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4215427-3 |
| title | Wavelets and other orthogonal systems with applications |
| title_auth | Wavelets and other orthogonal systems with applications |
| title_exact_search | Wavelets and other orthogonal systems with applications |
| title_full | Wavelets and other orthogonal systems with applications Gilbert G. Walter |
| title_fullStr | Wavelets and other orthogonal systems with applications Gilbert G. Walter |
| title_full_unstemmed | Wavelets and other orthogonal systems with applications Gilbert G. Walter |
| title_short | Wavelets and other orthogonal systems with applications |
| title_sort | wavelets and other orthogonal systems with applications |
| topic | Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Wavelet |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006655056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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