Weak weight-semi-greedy Markushevich bases

Autores
Berasategui, Miguel Hernán; Lassalle, Silvia Beatriz
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The main purpose of this paper is to study weight-semi-greedy Markushevich bases, and in particular, find conditions under which such bases are weight-almost greedy. In this context, we prove that, for a large class of weights, the two notions are equivalent. We also show that all weight semi-greedy bases are truncation quasi-greedy and weight-superdemocratic. In all of the above cases, we also bring to the context of weights the weak greedy and Chebyshev greedy algorithms—which are frequently studied in the literature on greedy approximation. In the course of our work, a new property arises naturally and its relation with squeeze symmetric and bidemocratic bases is given. In addition, we study some parameters involving the weak thresholding and Chebyshevian greedy algorithms. Finally, we give examples of conditional bases with some of the weighted greedy-type conditions we study.
Fil: Berasategui, Miguel Hernán. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Lassalle, Silvia Beatriz. Universidad de San Andrés; 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
Materia
GREEDY-LIKE BASES
NON-LINEAR APPROXIMATION
SEMI-GREEDY VARIANTS
WEIGHT GREEDY ALGORIGTHM
BASES
GREEDY APPROXIMATION
WEIGHTS
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:11336/232897
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/232897
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Weak weight-semi-greedy Markushevich basesBerasategui, Miguel HernánLassalle, Silvia BeatrizGREEDY-LIKE BASESNON-LINEAR APPROXIMATIONSEMI-GREEDY VARIANTSWEIGHT GREEDY ALGORIGTHMBASESGREEDY APPROXIMATIONWEIGHTShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The main purpose of this paper is to study weight-semi-greedy Markushevich bases, and in particular, find conditions under which such bases are weight-almost greedy. In this context, we prove that, for a large class of weights, the two notions are equivalent. We also show that all weight semi-greedy bases are truncation quasi-greedy and weight-superdemocratic. In all of the above cases, we also bring to the context of weights the weak greedy and Chebyshev greedy algorithms—which are frequently studied in the literature on greedy approximation. In the course of our work, a new property arises naturally and its relation with squeeze symmetric and bidemocratic bases is given. In addition, we study some parameters involving the weak thresholding and Chebyshevian greedy algorithms. Finally, we give examples of conditional bases with some of the weighted greedy-type conditions we study.Fil: Berasategui, Miguel Hernán. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Lassalle, Silvia Beatriz. Universidad de San Andrés; 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"; ArgentinaCambridge University Press2023-06info: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/11336/232897Berasategui, Miguel Hernán; Lassalle, Silvia Beatriz; Weak weight-semi-greedy Markushevich bases; Cambridge University Press; Proceedings Of The Royal Society Of Edinburgh Section A-mathematics; 154; 2; 6-2023; 1-620308-21051473-7124CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/product/identifier/S0308210523000537/type/journal_articleinfo:eu-repo/semantics/altIdentifier/doi/10.1017/prm.2023.53info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2111.00693info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:11:50Zoai:ri.conicet.gov.ar:11336/232897instacron: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:34982025-09-03 10:11:50.414CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Weak weight-semi-greedy Markushevich bases
title Weak weight-semi-greedy Markushevich bases
spellingShingle Weak weight-semi-greedy Markushevich bases
Berasategui, Miguel Hernán
GREEDY-LIKE BASES
NON-LINEAR APPROXIMATION
SEMI-GREEDY VARIANTS
WEIGHT GREEDY ALGORIGTHM
BASES
GREEDY APPROXIMATION
WEIGHTS
title_short Weak weight-semi-greedy Markushevich bases
title_full Weak weight-semi-greedy Markushevich bases
title_fullStr Weak weight-semi-greedy Markushevich bases
title_full_unstemmed Weak weight-semi-greedy Markushevich bases
title_sort Weak weight-semi-greedy Markushevich bases
dc.creator.none.fl_str_mv Berasategui, Miguel Hernán
Lassalle, Silvia Beatriz
author Berasategui, Miguel Hernán
author_facet Berasategui, Miguel Hernán
Lassalle, Silvia Beatriz
author_role author
author2 Lassalle, Silvia Beatriz
author2_role author
dc.subject.none.fl_str_mv GREEDY-LIKE BASES
NON-LINEAR APPROXIMATION
SEMI-GREEDY VARIANTS
WEIGHT GREEDY ALGORIGTHM
BASES
GREEDY APPROXIMATION
WEIGHTS
topic GREEDY-LIKE BASES
NON-LINEAR APPROXIMATION
SEMI-GREEDY VARIANTS
WEIGHT GREEDY ALGORIGTHM
BASES
GREEDY APPROXIMATION
WEIGHTS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The main purpose of this paper is to study weight-semi-greedy Markushevich bases, and in particular, find conditions under which such bases are weight-almost greedy. In this context, we prove that, for a large class of weights, the two notions are equivalent. We also show that all weight semi-greedy bases are truncation quasi-greedy and weight-superdemocratic. In all of the above cases, we also bring to the context of weights the weak greedy and Chebyshev greedy algorithms—which are frequently studied in the literature on greedy approximation. In the course of our work, a new property arises naturally and its relation with squeeze symmetric and bidemocratic bases is given. In addition, we study some parameters involving the weak thresholding and Chebyshevian greedy algorithms. Finally, we give examples of conditional bases with some of the weighted greedy-type conditions we study.
Fil: Berasategui, Miguel Hernán. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Lassalle, Silvia Beatriz. Universidad de San Andrés; 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
description The main purpose of this paper is to study weight-semi-greedy Markushevich bases, and in particular, find conditions under which such bases are weight-almost greedy. In this context, we prove that, for a large class of weights, the two notions are equivalent. We also show that all weight semi-greedy bases are truncation quasi-greedy and weight-superdemocratic. In all of the above cases, we also bring to the context of weights the weak greedy and Chebyshev greedy algorithms—which are frequently studied in the literature on greedy approximation. In the course of our work, a new property arises naturally and its relation with squeeze symmetric and bidemocratic bases is given. In addition, we study some parameters involving the weak thresholding and Chebyshevian greedy algorithms. Finally, we give examples of conditional bases with some of the weighted greedy-type conditions we study.
publishDate 2023
dc.date.none.fl_str_mv 2023-06
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/11336/232897
Berasategui, Miguel Hernán; Lassalle, Silvia Beatriz; Weak weight-semi-greedy Markushevich bases; Cambridge University Press; Proceedings Of The Royal Society Of Edinburgh Section A-mathematics; 154; 2; 6-2023; 1-62
0308-2105
1473-7124
CONICET Digital
CONICET
url http://hdl.handle.net/11336/232897
identifier_str_mv Berasategui, Miguel Hernán; Lassalle, Silvia Beatriz; Weak weight-semi-greedy Markushevich bases; Cambridge University Press; Proceedings Of The Royal Society Of Edinburgh Section A-mathematics; 154; 2; 6-2023; 1-62
0308-2105
1473-7124
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://www.cambridge.org/core/product/identifier/S0308210523000537/type/journal_article
info:eu-repo/semantics/altIdentifier/doi/10.1017/prm.2023.53
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2111.00693
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 Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
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 13.13397

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