Bases of Wavelets and Multiresolution in Analysis on Wiener Space
The multiresolution analysis is applied into the space of square integrable Wiener functionals for extending well-known constructions of orthonormal wavelets in L2(R) to this space denoted by L2 (μ), μ being the Wiener measure, as for instance Mallat’s construction or furthermore Goodman–Lee and Tan...
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| Formato: | Capítulo de libro |
| Lenguaje: | inglés |
| Publicado: |
IntechOpen
2022
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| Acceso en línea: | https://www.intechopen.com/chapters/84290 |
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| Sumario: | The multiresolution analysis is applied into the space of square integrable Wiener functionals for extending well-known constructions of orthonormal wavelets in L2(R) to this space denoted by L2 (μ), μ being the Wiener measure, as for instance Mallat’s construction or furthermore Goodman–Lee and Tang construction. We also extend the Calderon–Zygmund decomposition theorem into the L1(μ) framework. Even if L1-spaces do not have unconditional bases, wavelets still outperform Fourier analysis in some sense. We illustrate this by introducing periodized Wiener wavelets. |
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| ISBN: | 978-1-80355-738-0 |
| DOI: | 10.5772/intechopen.104713 |