Methods of applied Fourier analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Boston [u.a.]
Birkhäuser
1998
|
| Series: | Applied and numerical harmonic analysis
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 323 - 327 |
| Physical Description: | XII, 329 S. graph. Darst. |
| ISBN: | 3764339632 0817639632 |
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| 245 | 1 | 0 | |a Methods of applied Fourier analysis |c Jayakumar Ramanathan |
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Record in the Search Index
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| adam_text | Contents
Preface xi
1 Periodic Functions 1
1.1 The Characters 1
1.2 Some Tools of the Trade 4
1.3 Fourier Series: W Theory 8
1.4 Fourier Series: L2 Theory 15
1.5 Fourier Analysis of Measures 19
1.6 Smoothness and Decay of Fourier Series 22
1.7 Translation Invariant Operators 23
1.8 Problems 27
2 Hardy Spaces 31
2.1 Hardy Spaces and Invariant Subspaces 31
2.2 Boundary Values of Harmonic Functions 36
2.3 Hardy Spaces and Analytic Functions 42
2.4 The Structure of Inner Functions 45
2.5 The H1 Case 50
2.6 The Szego Kolmogorov Theorem 53
2.7 Problems 59
3 Prediction Theory 63
3.1 Introduction to Stationary Random Processes 63
3.2 Examples of Stationary Processes 68
3.3 The Reproducing Kernel 71
3.4 Spectral Estimation and Prediction 76
3.5 Problems 84
4 Discrete Systems and Control Theory 87
4.1 Introduction to System Theory 87
4.2 Translation Invariant Operators 90
4.3 H°° Control Theory 93
4.4 The Nehari Problem 103
4.5 Commutant Lifting and Interpolation 108
4.6 Proof of the Commutant Lifting Theorem 112
4.7 Problems 119
5 Harmonic Analysis in Euclidean Space 123
5.1 Function Spaces on Rn 123
5.2 The Fourier Transform on L1 127
5.3 Convolution and Approximation 134
5.4 The Fourier Transform: L2 Theory 138
5.5 Fourier Transform of Measures 145
5.6 Bochner s Theorem 152
5.7 Problems 156
6 Distributions 159
6.1 General Distributions 159
6.2 Two Theorems on Distributions 164
6.3 Schwartz Space 172
6.4 Tempered Distributions 175
6.5 Sobolev Spaces 179
6.6 Problems 184
7 Functions with Restricted Transforms 187
7.1 General Definitions and
the Sampling Formula 187
7.2 The Paley Wiener Theorem 192
7.3 Sampling Band Limited Functions 199
7.4 Band Limited Functions and Information 203
7.5 Problems 215
8 Phase Space 219
8.1 The Uncertainty Principle 219
8.2 The Ambiguity Function 227
8.3 Phase Space and Orthonormal Bases 236
8.4 The Zak Transform and the Wilson Basis 243
8.5 An Approximation Theorem 256
8.6 Problems 260
viii
9 Wavelet Analysis 263
9.1 Multiresolution Approximations 263
9.2 Wavelet Bases 267
9.3 Examples 276
9.4 Compactly Supported Wavelets 281
9.5 Compactly Supported Wavelets II 290
9.6 Problems 299
A The Discrete Fourier Transform 301
A.I The Analysis of Periodic Sequences 301
A.2 The Cooley Tukey Algorithm 306
A.3 The Good Winograd Algorithm 310
A.4 Fast Computations of Integrals 313
B The Her mite Functions 317
Bibliography 323
Index 328
ix
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| id | DE-604.BV012212089 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:23:41Z |
| institution | BVB |
| isbn | 3764339632 0817639632 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008276127 |
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| physical | XII, 329 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Applied and numerical harmonic analysis |
| spelling | Ramanathan, Jayakumar 1958- Verfasser (DE-588)120506513 aut Methods of applied Fourier analysis Jayakumar Ramanathan Boston [u.a.] Birkhäuser 1998 XII, 329 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied and numerical harmonic analysis Literaturverz. S. 323 - 327 Harmonische Analyse Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008276127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ramanathan, Jayakumar 1958- Methods of applied Fourier analysis Harmonische Analyse Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 |
| title | Methods of applied Fourier analysis |
| title_auth | Methods of applied Fourier analysis |
| title_exact_search | Methods of applied Fourier analysis |
| title_full | Methods of applied Fourier analysis Jayakumar Ramanathan |
| title_fullStr | Methods of applied Fourier analysis Jayakumar Ramanathan |
| title_full_unstemmed | Methods of applied Fourier analysis Jayakumar Ramanathan |
| title_short | Methods of applied Fourier analysis |
| title_sort | methods of applied fourier analysis |
| topic | Harmonische Analyse Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Harmonische Analyse |
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