Pointwise convergence to the initial data for nonlocal dyadic diffusions

In this paper we solve the initial value problem for the diffusion induced by dyadic fractional derivative s in R +. First we obtain the spectral analysis of the dyadic fractional derivative operator in terms of the Haar system, which unveils a structure for the underlying “heat kernel”. We show tha...

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Detalles Bibliográficos
Autores: Actis, Marcelo Jesús, Aimar, Hugo Alejandro
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/30630
Acceso en línea:http://hdl.handle.net/11336/30630
Access Level:acceso abierto
Palabra clave:pointwise convergence
nonlocal diffusion
dyadic fractional derivatives
Haar bases
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Pointwise convergence to the initial data for nonlocal dyadic diffusionsActis, Marcelo JesúsAimar, Hugo Alejandropointwise convergencenonlocal diffusiondyadic fractional derivativesHaar baseshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we solve the initial value problem for the diffusion induced by dyadic fractional derivative s in R +. First we obtain the spectral analysis of the dyadic fractional derivative operator in terms of the Haar system, which unveils a structure for the underlying “heat kernel”. We show that this kernel admits an integrable and decreasing majorant that involves the dyadic distance. This allows us to provide an estimate of the maximal operator of the diffusion by the Hardy-Littlewood dyadic maximal operator. As a consequence we obtain the pointwise convergence to the initial data.Fil: Actis, Marcelo Jesús. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaSpringer Heidelberg2016-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/30630Actis, Marcelo Jesús; Aimar, Hugo Alejandro; Pointwise convergence to the initial data for nonlocal dyadic diffusions; Springer Heidelberg; Czechoslovak Mathematical Journal; 66; 1; 3-2016; 193-2040011-4642CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs10587-016-0249-yinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10587-016-0249-yinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:46:48Zoai:ri.conicet.gov.ar:11336/30630instacron: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:34982024-05-08 13:46:49.021CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Pointwise convergence to the initial data for nonlocal dyadic diffusions
title Pointwise convergence to the initial data for nonlocal dyadic diffusions
spellingShingle Pointwise convergence to the initial data for nonlocal dyadic diffusions
Actis, Marcelo Jesús
pointwise convergence
nonlocal diffusion
dyadic fractional derivatives
Haar bases
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Pointwise convergence to the initial data for nonlocal dyadic diffusions
title_full Pointwise convergence to the initial data for nonlocal dyadic diffusions
title_fullStr Pointwise convergence to the initial data for nonlocal dyadic diffusions
title_full_unstemmed Pointwise convergence to the initial data for nonlocal dyadic diffusions
title_sort Pointwise convergence to the initial data for nonlocal dyadic diffusions
dc.creator.none.fl_str_mv Actis, Marcelo Jesús
Aimar, Hugo Alejandro
author Actis, Marcelo Jesús
author_facet Actis, Marcelo Jesús
Aimar, Hugo Alejandro
author_role author
author2 Aimar, Hugo Alejandro
author2_role author
dc.subject.none.fl_str_mv pointwise convergence
nonlocal diffusion
dyadic fractional derivatives
Haar bases
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic pointwise convergence
nonlocal diffusion
dyadic fractional derivatives
Haar bases
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description In this paper we solve the initial value problem for the diffusion induced by dyadic fractional derivative s in R +. First we obtain the spectral analysis of the dyadic fractional derivative operator in terms of the Haar system, which unveils a structure for the underlying “heat kernel”. We show that this kernel admits an integrable and decreasing majorant that involves the dyadic distance. This allows us to provide an estimate of the maximal operator of the diffusion by the Hardy-Littlewood dyadic maximal operator. As a consequence we obtain the pointwise convergence to the initial data.
publishDate 2016
dc.date.none.fl_str_mv 2016-03
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/11336/30630
Actis, Marcelo Jesús; Aimar, Hugo Alejandro; Pointwise convergence to the initial data for nonlocal dyadic diffusions; Springer Heidelberg; Czechoslovak Mathematical Journal; 66; 1; 3-2016; 193-204
0011-4642
CONICET Digital
CONICET
url http://hdl.handle.net/11336/30630
identifier_str_mv Actis, Marcelo Jesús; Aimar, Hugo Alejandro; Pointwise convergence to the initial data for nonlocal dyadic diffusions; Springer Heidelberg; Czechoslovak Mathematical Journal; 66; 1; 3-2016; 193-204
0011-4642
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs10587-016-0249-y
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10587-016-0249-y
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Heidelberg
publisher.none.fl_str_mv Springer Heidelberg
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,811543

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