Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
In this article we construct affine systems that provide a simultaneous atomic decomposition for a wide class of functional spaces including the Lebesgue spaces Lp(Rd), 1 < p < + ∞. The novelty and difficulty of this construction is that we allow for non-lattice translations.We prove that for...
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| Autores principales: | , , |
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| Formato: | Artículo publishedVersion |
| Lenguaje: | Inglés |
| Publicado: |
2013
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| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00018708_v232_n1_p98_Cabrelli |
| Aporte de: |
| Sumario: | In this article we construct affine systems that provide a simultaneous atomic decomposition for a wide class of functional spaces including the Lebesgue spaces Lp(Rd), 1 < p < + ∞. The novelty and difficulty of this construction is that we allow for non-lattice translations.We prove that for an arbitrary expansive matrix A and any set Λ-satisfying a certain spreadness condition but otherwise irregular-there exists a smooth window whose translations along the elements of Λ and dilations by powers of A provide an atomic decomposition for the whole range of the anisotropic Triebel-Lizorkin spaces. The generating window can be either chosen to be bandlimited or to have compact support.To derive these results we start with a known general "painless" construction that has recently appeared in the literature. We show that this construction extends to Besov and Triebel-Lizorkin spaces by providing adequate dual systems. © 2012 Elsevier Ltd. |
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