Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures

Autores
Antezana, Jorge Abel; García, María Guadalupe
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let μ be a probability measure on T that is singular with respect to the Haar measure. In this paper we study Fourier expansions in L2(T,μ) using techniques from the theory of model subspaces of the Hardy space. Since the sequence of monomials {zn}n∈N is effective in L2(T,μ), it has a Parseval frame associated via the Kaczmarz algorithm. Our first main goal is to identify the aforementioned frame with boundary values of the frame Pφ(zn) for the model subspace H(φ)=H2⊖φH2, where Pφ is the orthogonal projection from the Hardy space H2 onto H(φ). The study of Fourier expansions in L2(T,μ) also leads to consider positive kernels in the Hardy space. Our second main goal is to study the set of measures μ which reproduce a kernel contained in a model subspace. We completely characterize this set when the kernel is the reproducing kernel of a model subspace, and we study the consequences of this characterization.
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentina
Fil: García, María Guadalupe. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentina
Materia
FOURIER EXPANSIONS
KACZMARZ ALGORITHM
MODEL SUBSPACES
PARSEVAL FRAMES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/119698
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/119698
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measuresAntezana, Jorge AbelGarcía, María GuadalupeFOURIER EXPANSIONSKACZMARZ ALGORITHMMODEL SUBSPACESPARSEVAL FRAMEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let μ be a probability measure on T that is singular with respect to the Haar measure. In this paper we study Fourier expansions in L2(T,μ) using techniques from the theory of model subspaces of the Hardy space. Since the sequence of monomials {zn}n∈N is effective in L2(T,μ), it has a Parseval frame associated via the Kaczmarz algorithm. Our first main goal is to identify the aforementioned frame with boundary values of the frame Pφ(zn) for the model subspace H(φ)=H2⊖φH2, where Pφ is the orthogonal projection from the Hardy space H2 onto H(φ). The study of Fourier expansions in L2(T,μ) also leads to consider positive kernels in the Hardy space. Our second main goal is to study the set of measures μ which reproduce a kernel contained in a model subspace. We completely characterize this set when the kernel is the reproducing kernel of a model subspace, and we study the consequences of this characterization.Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; ArgentinaFil: García, María Guadalupe. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; ArgentinaAcademic Press Inc Elsevier Science2020-12info: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/11336/119698Antezana, Jorge Abel; García, María Guadalupe; Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 279; 10; 12-2020; 1-200022-1236CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://linkinghub.elsevier.com/retrieve/pii/S0022123620302688info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2020.108725info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1907.08876info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:36:44Zoai:ri.conicet.gov.ar:11336/119698instacron: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 10:36:44.815CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures
title Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures
spellingShingle Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures
Antezana, Jorge Abel
FOURIER EXPANSIONS
KACZMARZ ALGORITHM
MODEL SUBSPACES
PARSEVAL FRAMES
title_short Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures
title_full Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures
title_fullStr Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures
title_full_unstemmed Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures
title_sort Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures
dc.creator.none.fl_str_mv Antezana, Jorge Abel
García, María Guadalupe
author Antezana, Jorge Abel
author_facet Antezana, Jorge Abel
García, María Guadalupe
author_role author
author2 García, María Guadalupe
author2_role author
dc.subject.none.fl_str_mv FOURIER EXPANSIONS
KACZMARZ ALGORITHM
MODEL SUBSPACES
PARSEVAL FRAMES
topic FOURIER EXPANSIONS
KACZMARZ ALGORITHM
MODEL SUBSPACES
PARSEVAL FRAMES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let μ be a probability measure on T that is singular with respect to the Haar measure. In this paper we study Fourier expansions in L2(T,μ) using techniques from the theory of model subspaces of the Hardy space. Since the sequence of monomials {zn}n∈N is effective in L2(T,μ), it has a Parseval frame associated via the Kaczmarz algorithm. Our first main goal is to identify the aforementioned frame with boundary values of the frame Pφ(zn) for the model subspace H(φ)=H2⊖φH2, where Pφ is the orthogonal projection from the Hardy space H2 onto H(φ). The study of Fourier expansions in L2(T,μ) also leads to consider positive kernels in the Hardy space. Our second main goal is to study the set of measures μ which reproduce a kernel contained in a model subspace. We completely characterize this set when the kernel is the reproducing kernel of a model subspace, and we study the consequences of this characterization.
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentina
Fil: García, María Guadalupe. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de la Plata. Facultad de Cs.exactas. Centro de Matematica de la Plata.; Argentina
description Let μ be a probability measure on T that is singular with respect to the Haar measure. In this paper we study Fourier expansions in L2(T,μ) using techniques from the theory of model subspaces of the Hardy space. Since the sequence of monomials {zn}n∈N is effective in L2(T,μ), it has a Parseval frame associated via the Kaczmarz algorithm. Our first main goal is to identify the aforementioned frame with boundary values of the frame Pφ(zn) for the model subspace H(φ)=H2⊖φH2, where Pφ is the orthogonal projection from the Hardy space H2 onto H(φ). The study of Fourier expansions in L2(T,μ) also leads to consider positive kernels in the Hardy space. Our second main goal is to study the set of measures μ which reproduce a kernel contained in a model subspace. We completely characterize this set when the kernel is the reproducing kernel of a model subspace, and we study the consequences of this characterization.
publishDate 2020
dc.date.none.fl_str_mv 2020-12
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/11336/119698
Antezana, Jorge Abel; García, María Guadalupe; Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 279; 10; 12-2020; 1-20
0022-1236
CONICET Digital
CONICET
url http://hdl.handle.net/11336/119698
identifier_str_mv Antezana, Jorge Abel; García, María Guadalupe; Model subspaces techniques to study Fourier expansions in L^2 spaces associated to singular measures; Academic Press Inc Elsevier Science; Journal of Functional Analysis; 279; 10; 12-2020; 1-20
0022-1236
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://linkinghub.elsevier.com/retrieve/pii/S0022123620302688
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2020.108725
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1907.08876
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
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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 13.070432

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