A first course on wavelets:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
1996
|
| Schriftenreihe: | Studies in advanced mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | 489 S. Illustrationen, Diagramme |
| ISBN: | 0849382742 |
Internformat
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Datensatz im Suchindex
| DE-BY-862_location | 2000 |
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| adam_text | IMAGE 1
A FIRST COURSE ON
WAVELETS
EUGENIO HERNAENDEZ UNIVERSIDAD AUTONOMA DE MADRID GUIDO WEISS WASHINGTON
UNIVERSITY IN ST. LOUIS CRC PRESS BOCA RATON NEW YORK LONDON TOKYO
IMAGE 2
CONTENTS
1 BASES FOR L 2 (R) 1
1.1 PRELIMINARIES 2
1.2 ORTHONORMAL BASES GENERATED BY A SINGLE FUNCTION; THE BALIANLOW
THEOREM 7
1.3 SMOOTH PROJECTIONS ON L 2 (K) 11
1.4 LOCAL SINE AND COSINE BASES AND THE CONSTRUCTION OF SOME
WAVELETS 20
1.5 THE UNITARY FOLDING OPERATORS AND THE SMOOTH PROJECTIONS . 31
1.6 NOTES AND REFERENCES 40
2 MULTIRESOLUTION ANALYSIS AND THE CONSTRUCTION OF WAVELETS 43
2.1 MULTIRESOLUTION ANALYSIS 44
2.2 CONSTRUCTION OF WAVELETS FROM A MULTIRESOLUTION ANALYSIS . . 52
2.3 THE CONSTRUCTION OF COMPACTLY SUPPORTED WAVELETS 68
2.4 BETTER ESTIMATES FOR THE SMOOTHNESS OF COMPACTLY SUPPORTED
WAVELETS 93
2.5 NOTES AND REFERENCES 98
3 BAND-LIMITED WAVELETS 101
3.1 ORTHONORMALITY 101
3.2 COMPLETENESS 105
IMAGE 3
3.3 THE LEMARIE-MEYER WAVELETS REVISITED 115
3.4 CHARACTERIZATION OF SOME BAND-LIMITED WAVELETS 123
3.5 NOTES AND REFERENCES 138
4 OTHER CONSTRUCTIONS OF WAVELETS 141
4.1 FRANKLIN WAVELETS ON THE REAL LINE 141
4.2 SPLINE WAVELETS ON THE REAL LINE 152
4.3 ORTHONORMAL BASES OF PIECEWISE LINEAR CONTINUOUS FUNCTIONS
FOR L T) 164
4.4 ORTHONORMAL BASES OF PERIODIC SPLINES 176
4.5 PERIODIZATION OF WAVELETS DEFINED ON THE REAL LINE 186
4.6 NOTES AND REFERENCES 193
5 REPRESENTATION OF FUNCTIONS BY WAVELETS 201
5.1 BASES FOR BANACH SPACES 201
5.2 UNCONDITIONAL BASES FOR BANACH SPACES 206
5.3 CONVERGENCE OF WAVELET EXPANSIONS IN L P (E) 217
5.4 POINTWISE CONVERGENCE OF WAVELET EXPANSIONS 225
5.5 H 1 AND BMO ON 1 230
5.6 WAVELETS AS UNCONDITIONAL BASES FOR H L (W) AND L P (E) WITH
1 P OO 237
5.7 NOTES AND REFERENCES 247
6 CHARACTERIZATIONS OF FUNCTION SPACES USING WAVELETS 255
6.1 WAVELETS AND SAMPLING THEOREMS 256
6.2 LITTLEWOOD-PALEY THEORY 260
6.3 NECESSARY TOOLS 267
6.4 THE LEBESGUE SPACES L (E) WITH 1 P OO 279
6.5 THE HARDY SPACE H R) 287
6.6 THE SOBOLEV SPACES , *(!), KP OO, S = 1,2,3, *** . .. 296
6.7 THE LIPSCHITZ SPACES A A (E), 0 A 1, AND THE ZYGMUND
CLASS A*(E) 313
IMAGE 4
6.8 NOTES AND REFERENCES 323
7 C H A R A C T E R I Z A T I O NS IN T HE T H E O RY OF WAVELETS 331
7.1 THE BASIC EQUATIONS 332
7.2 SOME APPLICATIONS OF THE BASIC EQUATIONS 348
7.3 THE CHARACTERIZATION OF MRA WAVELETS 354
7.4 A CHARACTERIZATION OF LOW-PASS FILTERS 365
7.5 A CHARACTERIZATION OF SCALING FUNCTIONS 381
7.6 NON-EXISTENCE OF SMOOTH WAVELETS IN H 2 (R) 386
7.7 NOTES AND REFERENCES 393
8 F R A M ES 397
8.1 THE RECONSTRUCTION FORMULA FOR FRAMES 398
8.2 THE BALIAN-LOW THEOREM FOR FRAMES 403
8.3 FRAMES FROM TRANSLATIONS AND DILATIONS 410
8.4 SMOOTH FRAMES FOR H 2 (R) 418
8.5 NOTES AND REFERENCES 419
9 DISCRETE TRANSFORMS AND ALGORITHMS 427
9.1 THE DISCRETE FOURIER TRANSFORM (DFT) AND THE FAST FOURIER
TRANSFORM (FFT) 427
9.2 THE DISCRETE COSINE TRANSFORM (DCT) AND THE FAST COSINE
TRANSFORM (FCT) 432
9.3 THE DISCRETE VERSION OF THE LOCAL SINE AND COSINE BASES . . . 436
9.4 DECOMPOSITION AND RECONSTRUCTION ALGORITHMS FOR WAVELETS . 442
9.5 WAVELET PACKETS 449
9.6 NOTES AND REFERENCES 464
REFERENCES 467
A U T H OR INDEX 479
INDEX 485
Contents 1 Bases for T2(K) 1 1.1 Preliminaries............................................................................. 1.2 Orthonormal bases generated by a single function; the Balian- 2 Low theorem............................................................................. 1.3 Smooth projections on L2(R) 1.4 7 11 .................................................. Local sine and cosine bases and the construction of some wavelets....................................................................................... 20 1.5 The unitary folding operators and the smooth projections . 31 1.6 Notes and references.......................................................... 40 2 Multiresolution analysis and the construction of wavelets 43 2.1 Multiresolution analysis.................................................... 2.2 Construction of wavelets from a multiresolution analysis . . 52 2.3 The construction of compactly supported wavelets........... 68 2.4 Better estimates for the smoothness of compactly supported 2.5 44 wavelets................................................................................. 93 Notes and references........................................................... 98 3 Band-limited wavelets 101 3.1 Orthonormality.................................................................... 101 3.2 Completeness....................................................................... 105
3.3 The Lemarié-Meyer wavelets revisited.................................. 115 3.4 Characterization of some band-limited wavelets................... 123 3.5 Notes and references................................................................. 138 4 Other constructions of wavelets 141 4.1 Franklin wavelets on the real line............................................ 141 4.2 Spline wavelets on the real line............................................... 152 4.3 Orthonormal bases of piecewise linear continuous functions for L2(T) .......................................................................... 164 4.4 Orthonormal bases of periodic splines ................................... 176 4.5 Periodization of wavelets defined on the real line................ 186 4.6 Notes and references.................................................................. 193 5 Representation of functions by wavelets 201 5.1 Bases for Banach spaces............................................................ 201 5.2 Unconditional bases for Banach spaces................................... 206 5.3 Convergence of wavelet expansions in LP(R).......................... 217 5.4 Pointwise convergence of wavelet expansions..............................225 5.5 H1 and BMO on R..................................................................... 5.6 230 Wavelets as unconditional bases for №(R) and LP(R) with l p oo........................................................................... 237 5.7 Notes and references.................................................................. 6 Characterizations of
function spaces using wavelets 247 255 6.1 Wavelets and sampling theorems............................................ 256 6.2 Littlewood-Paley theory............................................................ 260 6.3 Necessary tools........................................................................... 267 6.4 The Lebesgue spaces LP(R) with 1 p oo.......................... 279 6.5 The Hardy space W R)............................................................ 287 6.6 The Sobolev spaces LP,Í(R)։ 1 P °°!s = 1 2 3, ·■ · · ■ · 6.7 The Lipschitz spaces AQ(R), 0 a 1, and the Zygmund class A* (R) ........................................................................ 313 296
6.8 Notes and references................................................................. 7 Characterizations in the theory of wavelets 8 323 331 7.1 The basic equations ................................................................. 332 7.2 Some applications of the basic equations.............................. 348 7.3 The characterization of MRA wavelets................................. 354 7.4 A characterization of low-pass filters.................................... 365 7.5 A characterization of scaling functions................................. 381 7.6 Non-existence of smooth wavelets in №(R) ......................... 386 7.7 Notes and references................................................................. 393 Frames 397 8.1 The reconstruction formula for frames.................................. 398 8.2 The Balian-Low theorem for frames ..................................... 403 8.3 Rames from translations and dilations.................................. 410 8.4 Smooth frames for №(K) ....................................................... 418 8.5 Notes and references................................................................ 419 9 Discrete transforms andalgorithms 9.1 The discrete Fourier transform (DFT) and the fast Fourier transform (FFT).............................................................. 9.2 427 The discrete cosine transform (DCT) and the fast cosine transform (FCT).............................................................. 9.3 427 432 The discrete version of the local sine and cosine bases . . . 436 9.4 Decomposition and reconstruction
algorithms for wavelets . 442 Wavelet packets.......................................................................... 449 9.6 Notes and references................................................................. 464 9.5 References 467 Author index 479 Index 485
|
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| author | Hernández, Eugenio 1954- Weiss, Guido L. 1928-2022 |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-08-01T10:45:00Z |
| institution | BVB |
| isbn | 0849382742 |
| language | English |
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| physical | 489 S. Illustrationen, Diagramme |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Studies in advanced mathematics |
| spellingShingle | Hernández, Eugenio 1954- Weiss, Guido L. 1928-2022 A first course on wavelets Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4215427-3 |
| title | A first course on wavelets |
| title_auth | A first course on wavelets |
| title_exact_search | A first course on wavelets |
| title_full | A first course on wavelets Eugenio Hernández ; Guido Weiss |
| title_fullStr | A first course on wavelets Eugenio Hernández ; Guido Weiss |
| title_full_unstemmed | A first course on wavelets Eugenio Hernández ; Guido Weiss |
| title_short | A first course on wavelets |
| title_sort | a first course on wavelets |
| 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=007468054&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007468054&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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Inhaltsverzeichnis
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THWS Schweinfurt Zentralbibliothek Lesesaal
| Signatur: |
2000 SK 450 H557 |
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| Exemplar 1 | ausleihbar Verfügbar Bestellen |