A mathematical introduction to wavelets /:
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 wavelets from mul...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1997.
|
| Schriftenreihe: | London Mathematical Society student texts ;
37. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 wavelets from multiresolution analysis, the book presents in detail the most important wavelets: spline wavelets, Meyer's wavelets and wavelets with compact support. It then moves to the corresponding multivariable theory and gives genuine multivariable examples. Wavelet decompositions in Lp spaces, Hardy spaces and Besov spaces are discussed and wavelet characterisations of those spaces are provided. Also included are some additional topics like periodic wavelets or wavelets not associated with a multiresolution analysis. This will be an invaluable book for those wishing to learn about the mathematical foundations of wavelets. |
| Beschreibung: | 1 online resource (xii, 261 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 254-259) and index. |
| ISBN: | 9781107362444 110736244X 9780511623790 0511623798 |
Internformat
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| 245 | 1 | 2 | |a A mathematical introduction to wavelets / |c P. Wojtaszczyk. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 1997. | ||
| 300 | |a 1 online resource (xii, 261 pages) : |b illustrations | ||
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| 490 | 1 | |a London Mathematical Society student texts ; |v 37 | |
| 504 | |a Includes bibliographical references (pages 254-259) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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 wavelets from multiresolution analysis, the book presents in detail the most important wavelets: spline wavelets, Meyer's wavelets and wavelets with compact support. It then moves to the corresponding multivariable theory and gives genuine multivariable examples. Wavelet decompositions in Lp spaces, Hardy spaces and Besov spaces are discussed and wavelet characterisations of those spaces are provided. Also included are some additional topics like periodic wavelets or wavelets not associated with a multiresolution analysis. This will be an invaluable book for those wishing to learn about the mathematical foundations of wavelets. | ||
| 505 | 0 | |a Cover; Title; Copyright; Contents; Preface; 1 A small sample; 1.1 The Haar wavelet; 1.2 The Strömberg wavelet; 2 General constructions; 2.1 Basic concepts; 2.2 Multiresolution analyses; 2.3 From scaling function to multiresolution analysis; 2.4 Construction of wavelets; 2.5 Periodic wavelets; 3 Some important wavelets; 3.1 What to look for in a wavelet?; 3.2 Meyer's wavelets; 3.3 Spline wavelets; 3.3.1 Spline functions; 3.3.2 Spline wavelets; 3.3.3 Exponential decay of spline wavelets; 3.3.4 Exponential decay of spline wavelets -- another approach; 3.4 Unimodular wavelets | |
| 505 | 8 | |a 4 Compactly supported wavelets4.1 General constructions; 4.2 Smooth wavelets; 4.3 Bare hands construction; 5 Multivariable wavelets; 5.1 Tensor products; 5.1.1 Multidimensional notation; 5.2 Multiresolution analyses; 5.3 Examples of multiresolution analyses; 6 Function spaces; 6.1 Lp-spaces; 6.2 BMO and H1; 7 Unconditional convergence; 7.1 Unconditional convergence of series; 7.2 Unconditional bases; 7.3 Unconditional convergence in Lp spaces; 8 Wavelet bases in Lp and H1; 8.1 Projections associated with a multiresolution analysis; 8.2 Unconditional bases in Lp and H1; 8.3 Haar wavelets | |
| 505 | 8 | |a 8.4 Polynomial bases9 Wavelets and smoothness of functions; 9.1 Modulus of continuit; 9.2 Multiresolution analyses and moduli of continuity; 9.3 Compression of wavelet decompositions; Appendix; Bibliography; Index | |
| 650 | 0 | |a Wavelets (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh91006163 | |
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| author | Wojtaszczyk, Przemysław, 1940- |
| author_GND | http://id.loc.gov/authorities/names/n88291542 |
| author_facet | Wojtaszczyk, Przemysław, 1940- |
| author_role | |
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| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA403 |
| callnumber-raw | QA403.3 .W64 1997eb |
| callnumber-search | QA403.3 .W64 1997eb |
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| contents | Cover; Title; Copyright; Contents; Preface; 1 A small sample; 1.1 The Haar wavelet; 1.2 The Strömberg wavelet; 2 General constructions; 2.1 Basic concepts; 2.2 Multiresolution analyses; 2.3 From scaling function to multiresolution analysis; 2.4 Construction of wavelets; 2.5 Periodic wavelets; 3 Some important wavelets; 3.1 What to look for in a wavelet?; 3.2 Meyer's wavelets; 3.3 Spline wavelets; 3.3.1 Spline functions; 3.3.2 Spline wavelets; 3.3.3 Exponential decay of spline wavelets; 3.3.4 Exponential decay of spline wavelets -- another approach; 3.4 Unimodular wavelets 4 Compactly supported wavelets4.1 General constructions; 4.2 Smooth wavelets; 4.3 Bare hands construction; 5 Multivariable wavelets; 5.1 Tensor products; 5.1.1 Multidimensional notation; 5.2 Multiresolution analyses; 5.3 Examples of multiresolution analyses; 6 Function spaces; 6.1 Lp-spaces; 6.2 BMO and H1; 7 Unconditional convergence; 7.1 Unconditional convergence of series; 7.2 Unconditional bases; 7.3 Unconditional convergence in Lp spaces; 8 Wavelet bases in Lp and H1; 8.1 Projections associated with a multiresolution analysis; 8.2 Unconditional bases in Lp and H1; 8.3 Haar wavelets 8.4 Polynomial bases9 Wavelets and smoothness of functions; 9.1 Modulus of continuit; 9.2 Multiresolution analyses and moduli of continuity; 9.3 Compression of wavelet decompositions; Appendix; Bibliography; Index |
| ctrlnum | (OCoLC)831665043 |
| 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 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn831665043 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:14Z |
| institution | BVB |
| isbn | 9781107362444 110736244X 9780511623790 0511623798 |
| language | English |
| oclc_num | 831665043 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xii, 261 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society student texts ; |
| series2 | London Mathematical Society student texts ; |
| spelling | Wojtaszczyk, Przemysław, 1940- https://id.oclc.org/worldcat/entity/E39PCjqY74cF8GPMbhjMvKVcT3 http://id.loc.gov/authorities/names/n88291542 A mathematical introduction to wavelets / P. Wojtaszczyk. Cambridge ; New York : Cambridge University Press, 1997. 1 online resource (xii, 261 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society student texts ; 37 Includes bibliographical references (pages 254-259) and index. Print version record. 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 wavelets from multiresolution analysis, the book presents in detail the most important wavelets: spline wavelets, Meyer's wavelets and wavelets with compact support. It then moves to the corresponding multivariable theory and gives genuine multivariable examples. Wavelet decompositions in Lp spaces, Hardy spaces and Besov spaces are discussed and wavelet characterisations of those spaces are provided. Also included are some additional topics like periodic wavelets or wavelets not associated with a multiresolution analysis. This will be an invaluable book for those wishing to learn about the mathematical foundations of wavelets. Cover; Title; Copyright; Contents; Preface; 1 A small sample; 1.1 The Haar wavelet; 1.2 The Strömberg wavelet; 2 General constructions; 2.1 Basic concepts; 2.2 Multiresolution analyses; 2.3 From scaling function to multiresolution analysis; 2.4 Construction of wavelets; 2.5 Periodic wavelets; 3 Some important wavelets; 3.1 What to look for in a wavelet?; 3.2 Meyer's wavelets; 3.3 Spline wavelets; 3.3.1 Spline functions; 3.3.2 Spline wavelets; 3.3.3 Exponential decay of spline wavelets; 3.3.4 Exponential decay of spline wavelets -- another approach; 3.4 Unimodular wavelets 4 Compactly supported wavelets4.1 General constructions; 4.2 Smooth wavelets; 4.3 Bare hands construction; 5 Multivariable wavelets; 5.1 Tensor products; 5.1.1 Multidimensional notation; 5.2 Multiresolution analyses; 5.3 Examples of multiresolution analyses; 6 Function spaces; 6.1 Lp-spaces; 6.2 BMO and H1; 7 Unconditional convergence; 7.1 Unconditional convergence of series; 7.2 Unconditional bases; 7.3 Unconditional convergence in Lp spaces; 8 Wavelet bases in Lp and H1; 8.1 Projections associated with a multiresolution analysis; 8.2 Unconditional bases in Lp and H1; 8.3 Haar wavelets 8.4 Polynomial bases9 Wavelets and smoothness of functions; 9.1 Modulus of continuit; 9.2 Multiresolution analyses and moduli of continuity; 9.3 Compression of wavelet decompositions; Appendix; Bibliography; Index Wavelets (Mathematics) http://id.loc.gov/authorities/subjects/sh91006163 Ondelettes. MATHEMATICS Infinity. bisacsh Wavelets (Mathematics) fast Wavelet gnd http://d-nb.info/gnd/4215427-3 SÉRIES ORTOGONAIS. larpcal Ondelettes (mathématiques) ram Ondelettes Utilisation. ram Ondelettes Problèmes et exercices. ram Espaces fonctionnels. ram Hardy, Espaces de. ram Besov, Espaces de. ram Espaces Lp. ram Print version: Wojtaszczyk, Przemysław, 1940- Mathematical introduction to wavelets. Cambridge ; New York : Cambridge University Press, 1997 0521570204 (DLC) 96037157 (OCoLC)35785649 London Mathematical Society student texts ; 37. http://id.loc.gov/authorities/names/n84727069 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=551356 Volltext |
| spellingShingle | Wojtaszczyk, Przemysław, 1940- A mathematical introduction to wavelets / London Mathematical Society student texts ; Cover; Title; Copyright; Contents; Preface; 1 A small sample; 1.1 The Haar wavelet; 1.2 The Strömberg wavelet; 2 General constructions; 2.1 Basic concepts; 2.2 Multiresolution analyses; 2.3 From scaling function to multiresolution analysis; 2.4 Construction of wavelets; 2.5 Periodic wavelets; 3 Some important wavelets; 3.1 What to look for in a wavelet?; 3.2 Meyer's wavelets; 3.3 Spline wavelets; 3.3.1 Spline functions; 3.3.2 Spline wavelets; 3.3.3 Exponential decay of spline wavelets; 3.3.4 Exponential decay of spline wavelets -- another approach; 3.4 Unimodular wavelets 4 Compactly supported wavelets4.1 General constructions; 4.2 Smooth wavelets; 4.3 Bare hands construction; 5 Multivariable wavelets; 5.1 Tensor products; 5.1.1 Multidimensional notation; 5.2 Multiresolution analyses; 5.3 Examples of multiresolution analyses; 6 Function spaces; 6.1 Lp-spaces; 6.2 BMO and H1; 7 Unconditional convergence; 7.1 Unconditional convergence of series; 7.2 Unconditional bases; 7.3 Unconditional convergence in Lp spaces; 8 Wavelet bases in Lp and H1; 8.1 Projections associated with a multiresolution analysis; 8.2 Unconditional bases in Lp and H1; 8.3 Haar wavelets 8.4 Polynomial bases9 Wavelets and smoothness of functions; 9.1 Modulus of continuit; 9.2 Multiresolution analyses and moduli of continuity; 9.3 Compression of wavelet decompositions; Appendix; Bibliography; Index Wavelets (Mathematics) http://id.loc.gov/authorities/subjects/sh91006163 Ondelettes. MATHEMATICS Infinity. bisacsh Wavelets (Mathematics) fast Wavelet gnd http://d-nb.info/gnd/4215427-3 SÉRIES ORTOGONAIS. larpcal Ondelettes (mathématiques) ram Ondelettes Utilisation. ram Ondelettes Problèmes et exercices. ram Espaces fonctionnels. ram Hardy, Espaces de. ram Besov, Espaces de. ram Espaces Lp. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh91006163 http://d-nb.info/gnd/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 | mathematical introduction to wavelets |
| topic | Wavelets (Mathematics) http://id.loc.gov/authorities/subjects/sh91006163 Ondelettes. MATHEMATICS Infinity. bisacsh Wavelets (Mathematics) fast Wavelet gnd http://d-nb.info/gnd/4215427-3 SÉRIES ORTOGONAIS. larpcal Ondelettes (mathématiques) ram Ondelettes Utilisation. ram Ondelettes Problèmes et exercices. ram Espaces fonctionnels. ram Hardy, Espaces de. ram Besov, Espaces de. ram Espaces Lp. ram |
| topic_facet | Wavelets (Mathematics) Ondelettes. MATHEMATICS Infinity. Wavelet SÉRIES ORTOGONAIS. Ondelettes (mathématiques) Ondelettes Utilisation. Ondelettes Problèmes et exercices. Espaces fonctionnels. Hardy, Espaces de. Besov, Espaces de. Espaces Lp. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=551356 |
| work_keys_str_mv | AT wojtaszczykprzemysław amathematicalintroductiontowavelets AT wojtaszczykprzemysław mathematicalintroductiontowavelets |