| Description |
1 online resource (xii, 261 pages) : illustrations |
| Series |
London Mathematical Society student texts ; 37 |
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London Mathematical Society student texts ; 37.
|
| 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 |
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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 |
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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 |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 254-259) and index |
| Notes |
Print version record |
| Subject |
Wavelets (Mathematics)
|
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MATHEMATICS -- Infinity.
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Wavelets (Mathematics)
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Wavelet
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SÉRIES ORTOGONAIS.
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Ondelettes (mathématiques)
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Ondelettes -- Utilisation.
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Ondelettes -- Problèmes et exercices.
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Espaces fonctionnels.
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Hardy, Espaces de.
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Besov, Espaces de.
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Espaces Lp.
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| Form |
Electronic book
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| ISBN |
9781107362444 |
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110736244X |
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9780511623790 |
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0511623798 |
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