Haar wavelet characterization of dyadic lipschitz regularity
We obtain a necessary and sufficient condition on the Haar coefficients of a real function f defined on R+ for the Lipschitz α regularity of f with respect to the ultrametric δ(x, y) = inf{|I| : x, y ∈ I; I ∈ D}, where D is the family of all dyadic intervals in R+ and α is positive. Precisely, f ∈ L...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/217630 |
| Acceso en línea: | http://hdl.handle.net/11336/217630 |
| Access Level: | acceso abierto |
| Palabra clave: | HAAR BASES DYADIC ANALYSIS WAVELETS LIPSCHITZ REGULARITY https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We obtain a necessary and sufficient condition on the Haar coefficients of a real function f defined on R+ for the Lipschitz α regularity of f with respect to the ultrametric δ(x, y) = inf{|I| : x, y ∈ I; I ∈ D}, where D is the family of all dyadic intervals in R+ and α is positive. Precisely, f ∈ Lipδ (α) if and only if D f, hj k E ≤ C2 −(α+ 1 2 )j , for some constant C, every j ∈ Z and every k = 0, 1, 2, . . . Here, as usual h j k (x) = 2j/2h(2jx − k) and h(x) = X[0,1/2)(x) − X[1/2,1)(x). |
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