Greedy-like bases for sequences with gaps

Autores
Berasategui, Miguel Hernán; Berná, Pablo M.
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In 2018, Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the n-t-quasi-greedy property that is based on them. Building upon this foundation, our current work aims to further investigate these algorithms and bases while introducing new ideas for two primary purposes. First, we aim to prove that for  n with bounded quotient gaps, n-t-quasi-greedy bases are quasi-greedy bases. This generalization extends a previous result to the context of Markushevich bases and, also, completes the answer to a question by Oikhberg. The second objective is to extend certain approximation properties of the greedy algorithm to the context of sequences with gaps and study if there is a relationship between this new extension and the usual convergence.
Fil: Berasategui, Miguel Hernán. 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. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Berná, Pablo M.. Cunef Universidad; España
Materia
NON-LINEAR APPROXIMATION
GREEDY BASES
WEAK GREEDY ALGORITHM
QUASI-GREEDY BASES
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:11336/234649
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/234649
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Greedy-like bases for sequences with gapsBerasategui, Miguel HernánBerná, Pablo M.NON-LINEAR APPROXIMATIONGREEDY BASESWEAK GREEDY ALGORITHMQUASI-GREEDY BASEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In 2018, Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the n-t-quasi-greedy property that is based on them. Building upon this foundation, our current work aims to further investigate these algorithms and bases while introducing new ideas for two primary purposes. First, we aim to prove that for  n with bounded quotient gaps, n-t-quasi-greedy bases are quasi-greedy bases. This generalization extends a previous result to the context of Markushevich bases and, also, completes the answer to a question by Oikhberg. The second objective is to extend certain approximation properties of the greedy algorithm to the context of sequences with gaps and study if there is a relationship between this new extension and the usual convergence.Fil: Berasategui, Miguel Hernán. 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. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Berná, Pablo M.. Cunef Universidad; EspañaBirkhauser2024-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/234649Berasategui, Miguel Hernán; Berná, Pablo M.; Greedy-like bases for sequences with gaps; Birkhauser; Banach Journal of Mathematical Analysis; 18; 2; 2-2024; 1-432662-20331735-8787CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/10.1007/s43037-024-00324-2info:eu-repo/semantics/altIdentifier/doi/10.1007/s43037-024-00324-2info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2009.02257info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:21:46Zoai:ri.conicet.gov.ar:11336/234649instacron: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 10:21:46.818CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Greedy-like bases for sequences with gaps
title Greedy-like bases for sequences with gaps
spellingShingle Greedy-like bases for sequences with gaps
Berasategui, Miguel Hernán
NON-LINEAR APPROXIMATION
GREEDY BASES
WEAK GREEDY ALGORITHM
QUASI-GREEDY BASES
title_short Greedy-like bases for sequences with gaps
title_full Greedy-like bases for sequences with gaps
title_fullStr Greedy-like bases for sequences with gaps
title_full_unstemmed Greedy-like bases for sequences with gaps
title_sort Greedy-like bases for sequences with gaps
dc.creator.none.fl_str_mv Berasategui, Miguel Hernán
Berná, Pablo M.
author Berasategui, Miguel Hernán
author_facet Berasategui, Miguel Hernán
Berná, Pablo M.
author_role author
author2 Berná, Pablo M.
author2_role author
dc.subject.none.fl_str_mv NON-LINEAR APPROXIMATION
GREEDY BASES
WEAK GREEDY ALGORITHM
QUASI-GREEDY BASES
topic NON-LINEAR APPROXIMATION
GREEDY BASES
WEAK GREEDY ALGORITHM
QUASI-GREEDY BASES
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 2018, Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the n-t-quasi-greedy property that is based on them. Building upon this foundation, our current work aims to further investigate these algorithms and bases while introducing new ideas for two primary purposes. First, we aim to prove that for  n with bounded quotient gaps, n-t-quasi-greedy bases are quasi-greedy bases. This generalization extends a previous result to the context of Markushevich bases and, also, completes the answer to a question by Oikhberg. The second objective is to extend certain approximation properties of the greedy algorithm to the context of sequences with gaps and study if there is a relationship between this new extension and the usual convergence.
Fil: Berasategui, Miguel Hernán. 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. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Berná, Pablo M.. Cunef Universidad; España
description In 2018, Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the n-t-quasi-greedy property that is based on them. Building upon this foundation, our current work aims to further investigate these algorithms and bases while introducing new ideas for two primary purposes. First, we aim to prove that for  n with bounded quotient gaps, n-t-quasi-greedy bases are quasi-greedy bases. This generalization extends a previous result to the context of Markushevich bases and, also, completes the answer to a question by Oikhberg. The second objective is to extend certain approximation properties of the greedy algorithm to the context of sequences with gaps and study if there is a relationship between this new extension and the usual convergence.
publishDate 2024
dc.date.none.fl_str_mv 2024-02
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/11336/234649
Berasategui, Miguel Hernán; Berná, Pablo M.; Greedy-like bases for sequences with gaps; Birkhauser; Banach Journal of Mathematical Analysis; 18; 2; 2-2024; 1-43
2662-2033
1735-8787
CONICET Digital
CONICET
url http://hdl.handle.net/11336/234649
identifier_str_mv Berasategui, Miguel Hernán; Berná, Pablo M.; Greedy-like bases for sequences with gaps; Birkhauser; Banach Journal of Mathematical Analysis; 18; 2; 2-2024; 1-43
2662-2033
1735-8787
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://link.springer.com/10.1007/s43037-024-00324-2
info:eu-repo/semantics/altIdentifier/doi/10.1007/s43037-024-00324-2
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2009.02257
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
dc.publisher.none.fl_str_mv Birkhauser
publisher.none.fl_str_mv Birkhauser
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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