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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1997.
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| Colección: | London Mathematical Society student texts ;
37. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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