Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces

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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: Cabrelli, C., Molter, U., Romero, J.L.
Formato: JOUR
Materias:
Affine systems
Anisotropic function spaces
Besov spaces
Non-uniform atomic decomposition
Triebel-Lizorkin spaces
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00018708_v232_n1_p98_Cabrelli
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00018708_v232_n1_p98_Cabrelli
record_format dspace
spelling todo:paper_00018708_v232_n1_p98_Cabrelli2023-10-03T13:52:19Z Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces Cabrelli, C. Molter, U. Romero, J.L. Affine systems Anisotropic function spaces Besov spaces Non-uniform atomic decomposition 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 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. Fil:Cabrelli, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Molter, U. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Romero, J.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00018708_v232_n1_p98_Cabrelli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Affine systems
Anisotropic function spaces
Besov spaces
Non-uniform atomic decomposition
Triebel-Lizorkin spaces
spellingShingle Affine systems
Anisotropic function spaces
Besov spaces
Non-uniform atomic decomposition
Triebel-Lizorkin spaces
Cabrelli, C.
Molter, U.
Romero, J.L.
Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
topic_facet Affine systems
Anisotropic function spaces
Besov spaces
Non-uniform atomic decomposition
Triebel-Lizorkin spaces
description 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.
format JOUR
author Cabrelli, C.
Molter, U.
Romero, J.L.
author_facet Cabrelli, C.
Molter, U.
Romero, J.L.
author_sort Cabrelli, C.
title Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
title_short Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
title_full Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
title_fullStr Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
title_full_unstemmed Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
title_sort non-uniform painless decompositions for anisotropic besov and triebel-lizorkin spaces
url http://hdl.handle.net/20.500.12110/paper_00018708_v232_n1_p98_Cabrelli
work_keys_str_mv AT cabrellic nonuniformpainlessdecompositionsforanisotropicbesovandtriebellizorkinspaces
AT molteru nonuniformpainlessdecompositionsforanisotropicbesovandtriebellizorkinspaces
AT romerojl nonuniformpainlessdecompositionsforanisotropicbesovandtriebellizorkinspaces
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