A mathematical introduction to wavelets:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Edition: | reprint., transferred to digital print. |
| Series: | London Mathematical Society: London Mathematical Society student texts
37 |
| Subjects: | |
| Online Access: | Klappentext Inhaltsverzeichnis |
| Physical Description: | XII, 261 S. |
| ISBN: | 9780521578943 0521578949 |
Staff View
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| 245 | 1 | 0 | |a A mathematical introduction to wavelets |c P. Wojtaszczyk |
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| 300 | |a XII, 261 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface Pa9e vii
1
A small sample I
1.1
The Haar
wavelet
1
1.2
The
Strömberg
wavelet
5
2
General constructions
17
2.1
Basic concepts
17
2.2
Multiresolution analyses
20
2.3
From scaling function to multiresolution analysis
26
2.4
Construction of wavelets
32
2.5
Periodic wavelets
38
3
Some important wavelets
46
3.1
What to look for in a wavelet?
46
3.2
Meyer s wavelets
49
3.3
Spline wavelets
51
3.3.1
Spline functions.
52
3.3.2
Spline wavelets
56
3.3.3
Exponential decay of spline wavelets
58
3.3.4
Exponential decay of spline wavelets
-
another approach
61
3.4
Unimodular wavelets
65
4
Compactly supported wavelets
75
4.1
General constructions
75
4.2
Smooth wavelets
83
4.3
Bare hands construction
90
5 Multivariable
wavelets
101
5.1
Tensor products
102
5.1.1
Multidimensional notation
105
5.2
Multiresolution analyses
106
5.3
Examples of multiresolution analyses
120
vi
Contents
6
Function spaces
140
6.1
Lp-spaces
140
6.2
BMO and Hi
148
7
Unconditional convergence
168
7.1
Unconditional convergence of series
168
7.2
Unconditional bases
173
7.3
Unconditional convergence in Lv spaces
175
8
Wavelet bases in Lp and H
181
8.1
Projections associated with a multiresolution analysis
182
8.2
Unconditional bases in Lv and H
191
8.3 Haar
wavelets
198
8.4
Polynomial bases
207
9
Wavelets and smoothness of functions
216
9.1
Modulus of continuity
216
9.2
Multiresolution analyses and moduli of continuity
222
9.3
Compression of wavelet decompositions
231
Appendix
239
Bibliography
254
Index
260
This book presents a mathematical
introduction
to the theory of orthogonal
wavelets and their uses in analysing functions and function spaces; both in
one and in several variables.
Starting with a detailed and self-contained discussion of the general
construction of one dimensional vvaveiets from multiresoiution analysis, the
book presents in detail the most important wavelets: spline wavelets,
Meyer s vvaveiets and vvaveiets with compact support. It then moves to the
corresponding
muttivariable
theory and gives genuine niultivariable examples.
Wavelet decompositions in L-spaces, Hardy spaces and
Besov
spaces are
discussed and wavelet characterisations of those spaces are provided. Also
included are some additional topics like periodic vvaveiets or vvaveiets not
associated with a multiresoiution analysis.
This will be an invaluable book for those wishing to learn about the
mathematical foundations of vvaveiets.
|
| any_adam_object | 1 |
| author | Wojtaszczyk, Przemysław 1940- |
| author_GND | (DE-588)143778927 |
| author_facet | Wojtaszczyk, Przemysław 1940- |
| author_role | aut |
| author_sort | Wojtaszczyk, Przemysław 1940- |
| author_variant | p w pw |
| building | Verbundindex |
| bvnumber | BV025504656 |
| classification_rvk | SK 450 |
| ctrlnum | (OCoLC)883968257 (DE-599)BVBBV025504656 |
| discipline | Mathematik |
| edition | reprint., transferred to digital print. |
| format | Book |
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| id | DE-604.BV025504656 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:35:29Z |
| institution | BVB |
| isbn | 9780521578943 0521578949 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020115687 |
| oclc_num | 883968257 |
| open_access_boolean | |
| owner | DE-11 DE-739 |
| owner_facet | DE-11 DE-739 |
| physical | XII, 261 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | London Mathematical Society: London Mathematical Society student texts |
| spelling | Wojtaszczyk, Przemysław 1940- Verfasser (DE-588)143778927 aut A mathematical introduction to wavelets P. Wojtaszczyk reprint., transferred to digital print. Cambridge [u.a.] Cambridge Univ. Press 2003 XII, 261 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society student texts 37 Wavelet (DE-588)4215427-3 gnd rswk-swf Wavelet (DE-588)4215427-3 s DE-604 London Mathematical Society London Mathematical Society student texts 37 (DE-604)BV000841726 37 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020115687&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020115687&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wojtaszczyk, Przemysław 1940- A mathematical introduction to wavelets Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4215427-3 |
| title | A mathematical introduction to wavelets |
| title_auth | A mathematical introduction to wavelets |
| title_exact_search | A mathematical introduction to wavelets |
| title_full | A mathematical introduction to wavelets P. Wojtaszczyk |
| title_fullStr | A mathematical introduction to wavelets P. Wojtaszczyk |
| title_full_unstemmed | A mathematical introduction to wavelets P. Wojtaszczyk |
| title_short | A mathematical introduction to wavelets |
| title_sort | a mathematical introduction to 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=020115687&sequence=000003&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=020115687&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000841726 |
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