Wavelets through a looking glass: the world of the spectrum
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2002
|
| Series: | Applied and numerical harmonic analysis
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 398 S. Ill., graph. Darst. |
| ISBN: | 0817642803 3764342803 |
Staff View
MARC
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Record in the Search Index
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| adam_text |
OLA BRATTELI PALLE JORGENSEN WAVELETS THROUGH A LOOKING GLASS THE WORLD
OF THE SPECTRUM WITH 147 ILLUSTRATIONS BY BRIAN TREADWAY BIRKHAUSER
BOSTON * BASEL * BERLIN CONTENTS PREFACE XI LIST OF FIGURES XVII LIST OF
TABLES XXI 1 INTRODUCTION 1 OVERTURE: WHY WAVELETS? 1 1.1 SUBBAND
FILTERS AND SIEVES 12 1.2 MATRIX FUNCTIONS AND MULTIRESOLUTIONS 16 1.3
QUBITS: THE ORACLE OF FEYNMAN AND THE ALGORITHM OF SHOR 25 1.4 CHAOS AND
CASCADE APPROXIMATION 38 1.5 SPECTRAL BOUNDS FOR THE TRANSFER AND
SUBDIVISION OPERATORS 39 1.6 CONNECTIONS TO GROUP THEORY 42 1.7 WAVELET
PACKETS 44 1.8 THE GABOR TRANSFORM 46 EXERCISES 47 TERMINOLOGY 73 2
HOMOTOPY THEORY AND CASCADES 79 THE DANGERS OF NAVIGATING THE LANDSCAPE
OF WAVELETS 79 2.1 HOMOTOPY CLASSES OF WAVELETS 82 2.2 MULTIRESOLUTION
ANALYSIS AND TIGHT FRAMES 91 2.3 GENERALITY OF MULTIRESOLUTION ANALYSIS
103 2.4 GLOBAL HOMOTOPY AND AN INDEX THEOREM 106 X CONTENTS 2.5 CASCADES
IN L 2 (R) 121 2.6 AN OPEN PROBLEM 134 EXERCISES 135 3 CAN YOU HEAR THE
SHAPE OF A WAVELET? 147 THE WORLD OF THE SPECTRUM 147 3.1 TRANSFER
OPERATORS 152 3.2 GALERKIN PROJECTIONS AND SPECTRA OF TRANSFER OPERATORS
156 3.3 SPECTRUM AND REGULARITY 165 3.4 THE SPECTRA OF RESTRICTIONS OF
THE TRANSFER OPERATOR 184 3.5 THE SPECTRAL RADIUS 193 EXERCISES 199 4
THE TRANSFER OPERATOR AND PERRON-FROBENIUS THEORY 203 A SLANTED MATRIX
FROM DYNAMICS 203 4.1 THE DUALITY BETWEEN KNEADING AND CHOPPING 205 4.2
A GREEN'S FUNCTION 214 4.3 THE PERRON-FROBENIUS EIGENFUNCTION 235 4.4
APPROXIMATION THEORY 242 4.5 ERGODIC MEANS 253 EXERCISES 260 5 THE FIXED
POINTS OF THE TRANSFER OPERATOR 265 THE FINE STRUCTURE OF CORRELATIONS
265 5.1 THE MINIMAL FUNCTION G SUCH THAT R (G) = G, 0 G 1, AND G (1)
= 1 . 267 5.2 THE C* -ALGEBRA KER (L - R\ C (J))'- ESTIMATES AND
IDENTITIES 278 5.3 INVERSE SPECTRAL THEORY 292 5.4 CYCLES 298 5.5 PURE
STATES 310 5.6 HISTORICAL NOTES AND REMARKS 318 EXERCISES 319 6
ORTHOGONALIZATION AND ISOSPECTRAL APPROXIMATION 325 THE OTHER SIDE OF
WAVELETS 325 6.1 EXAMPLES 328 6.2 SPECTRAL PROPERTIES OF BIORTHOGONAL
WAVELETS 336 6.3 ISOSPECTRAL APPROXIMATION 347 6.4 BIORTHOGONAL FRAMES:
MULTIRESOLUTION ANALYSIS AND INDEX THEOREM . . . . 358 EXERCISES 363
REFERENCES 369 INDEX 387 |
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| author | Bratteli, Ola Jørgensen, Palle E. T. 1947- |
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| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV014186985 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:39:04Z |
| institution | BVB |
| isbn | 0817642803 3764342803 |
| language | English |
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| physical | XIX, 398 S. Ill., graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Birkhäuser |
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| series2 | Applied and numerical harmonic analysis |
| spelling | Bratteli, Ola Verfasser aut Wavelets through a looking glass the world of the spectrum Ola Bratteli ; Palle Jorgensen Boston [u.a.] Birkhäuser 2002 XIX, 398 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied and numerical harmonic analysis Análise de ondaletas (wavelets) larpcal Ondelettes Spectre (Mathématiques) Spectral theory (Mathematics) Wavelets (Mathematics) Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Wavelet (DE-588)4215427-3 s DE-604 Spektraltheorie (DE-588)4116561-5 s Jørgensen, Palle E. T. 1947- Verfasser (DE-588)124805515 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009724552&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bratteli, Ola Jørgensen, Palle E. T. 1947- Wavelets through a looking glass the world of the spectrum Análise de ondaletas (wavelets) larpcal Ondelettes Spectre (Mathématiques) Spectral theory (Mathematics) Wavelets (Mathematics) Spektraltheorie (DE-588)4116561-5 gnd Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4215427-3 |
| title | Wavelets through a looking glass the world of the spectrum |
| title_auth | Wavelets through a looking glass the world of the spectrum |
| title_exact_search | Wavelets through a looking glass the world of the spectrum |
| title_full | Wavelets through a looking glass the world of the spectrum Ola Bratteli ; Palle Jorgensen |
| title_fullStr | Wavelets through a looking glass the world of the spectrum Ola Bratteli ; Palle Jorgensen |
| title_full_unstemmed | Wavelets through a looking glass the world of the spectrum Ola Bratteli ; Palle Jorgensen |
| title_short | Wavelets through a looking glass |
| title_sort | wavelets through a looking glass the world of the spectrum |
| title_sub | the world of the spectrum |
| topic | Análise de ondaletas (wavelets) larpcal Ondelettes Spectre (Mathématiques) Spectral theory (Mathematics) Wavelets (Mathematics) Spektraltheorie (DE-588)4116561-5 gnd Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Análise de ondaletas (wavelets) Ondelettes Spectre (Mathématiques) Spectral theory (Mathematics) Wavelets (Mathematics) Spektraltheorie Wavelet |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009724552&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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