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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/2825
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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 Técnicas2025-09-29T09:42:50Zoai: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:34982025-09-29 09:42:50.295CONICET 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 |
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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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13.070432 |