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

Autores
Cabrelli, Carlos; Molter, Ursula Maria; Romero, Jose Luis Fernando
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Romero, Jose Luis Fernando. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Materia
AFFINE SYSTEMS
ANISOTROPIC FUNCTION SPACES
BESOV SPACES
NON-UNIFORM ATOMIC DECOMPOSITION
TRIEBEL-LIZORKIN SPACES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/2825
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/2825
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spacesCabrelli, CarlosMolter, Ursula MariaRomero, Jose Luis FernandoAFFINE SYSTEMSANISOTROPIC FUNCTION SPACESBESOV SPACESNON-UNIFORM ATOMIC DECOMPOSITIONTRIEBEL-LIZORKIN SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In 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.Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Romero, Jose Luis Fernando. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaElsevier2013-01-15info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/2825Cabrelli, Carlos; Molter, Ursula Maria; Romero, Jose Luis Fernando; Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces; Elsevier; Advances in Mathematics; 232; 1; 15-1-2013; 98-1200001-8708enginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2012.09.026info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0001870812003581info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1108.2748info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:11:25Zoai:ri.conicet.gov.ar:11336/2825instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:11:26.189CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
title Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
spellingShingle Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
Cabrelli, Carlos
AFFINE SYSTEMS
ANISOTROPIC FUNCTION SPACES
BESOV SPACES
NON-UNIFORM ATOMIC DECOMPOSITION
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
dc.creator.none.fl_str_mv Cabrelli, Carlos
Molter, Ursula Maria
Romero, Jose Luis Fernando
author Cabrelli, Carlos
author_facet Cabrelli, Carlos
Molter, Ursula Maria
Romero, Jose Luis Fernando
author_role author
author2 Molter, Ursula Maria
Romero, Jose Luis Fernando
author2_role author
author
dc.subject.none.fl_str_mv AFFINE SYSTEMS
ANISOTROPIC FUNCTION SPACES
BESOV SPACES
NON-UNIFORM ATOMIC DECOMPOSITION
TRIEBEL-LIZORKIN SPACES
topic AFFINE SYSTEMS
ANISOTROPIC FUNCTION SPACES
BESOV SPACES
NON-UNIFORM ATOMIC DECOMPOSITION
TRIEBEL-LIZORKIN SPACES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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.
Fil: Cabrelli, Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Molter, Ursula Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Romero, Jose Luis Fernando. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
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.
publishDate 2013
dc.date.none.fl_str_mv 2013-01-15
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/2825
Cabrelli, Carlos; Molter, Ursula Maria; Romero, Jose Luis Fernando; Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces; Elsevier; Advances in Mathematics; 232; 1; 15-1-2013; 98-120
0001-8708
url http://hdl.handle.net/11336/2825
identifier_str_mv Cabrelli, Carlos; Molter, Ursula Maria; Romero, Jose Luis Fernando; Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces; Elsevier; Advances in Mathematics; 232; 1; 15-1-2013; 98-120
0001-8708
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2012.09.026
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0001870812003581
info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1108.2748
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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