Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces

Autores
Defant, A.; Galicer, Daniel Eric; Mansilla, Martin Ignacio; Masty?o, M; Muro, Luis Santiago Miguel
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The main aim of this work is to study important local Banach space constants for Boolean cube function spaces. Specifically, we focus on mathcal{B}_{mathcal{S}}^{N}, the finite-dimensional Banach space of all real-valued functions defined on the N-dimensional Boolean cube {-1, +1}^{N} that have Fourier–Walsh expansions supported on a fixed family of subsets of {1, ldots , N}⁠. Our investigation centers on the projection, Sidon, and Gordon–Lewis constants of this function space. We combine tools from different areas to derive exact formulas and asymptotic estimates of these parameters for special types of families depending on the dimension of the Boolean cube and other complexity characteristics of the support set ⁠. Using local Banach space theory, we establish the intimate relationship among these three important constants.
Fil: Defant, A.. Carl von Ossietzky Universität; Alemania
Fil: Galicer, Daniel Eric. 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: Mansilla, Martin Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Masty?o, M. Adam Mickiewicz University; Polonia
Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Materia
Projection constants
Boolean functions
local theory of Banach spaces
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:11336/257790
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/257790
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function SpacesDefant, A.Galicer, Daniel EricMansilla, Martin IgnacioMasty?o, MMuro, Luis Santiago MiguelProjection constantsBoolean functionslocal theory of Banach spaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The main aim of this work is to study important local Banach space constants for Boolean cube function spaces. Specifically, we focus on mathcal{B}_{mathcal{S}}^{N}, the finite-dimensional Banach space of all real-valued functions defined on the N-dimensional Boolean cube {-1, +1}^{N} that have Fourier–Walsh expansions supported on a fixed family of subsets of {1, ldots , N}⁠. Our investigation centers on the projection, Sidon, and Gordon–Lewis constants of this function space. We combine tools from different areas to derive exact formulas and asymptotic estimates of these parameters for special types of families depending on the dimension of the Boolean cube and other complexity characteristics of the support set ⁠. Using local Banach space theory, we establish the intimate relationship among these three important constants.Fil: Defant, A.. Carl von Ossietzky Universität; AlemaniaFil: Galicer, Daniel Eric. 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: Mansilla, Martin Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Masty?o, M. Adam Mickiewicz University; PoloniaFil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaOxford University Press2024-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/257790Defant, A.; Galicer, Daniel Eric; Mansilla, Martin Ignacio; Masty?o, M; Muro, Luis Santiago Miguel; Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces; Oxford University Press; International Mathematics Research Notices; 2024; 15; 8-2024; 11239-112701073-7928CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article/2024/15/11239/7687880info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnae083info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:19:44Zoai:ri.conicet.gov.ar:11336/257790instacron: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 10:19:45.023CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces
title Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces
spellingShingle Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces
Defant, A.
Projection constants
Boolean functions
local theory of Banach spaces
title_short Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces
title_full Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces
title_fullStr Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces
title_full_unstemmed Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces
title_sort Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces
dc.creator.none.fl_str_mv Defant, A.
Galicer, Daniel Eric
Mansilla, Martin Ignacio
Masty?o, M
Muro, Luis Santiago Miguel
author Defant, A.
author_facet Defant, A.
Galicer, Daniel Eric
Mansilla, Martin Ignacio
Masty?o, M
Muro, Luis Santiago Miguel
author_role author
author2 Galicer, Daniel Eric
Mansilla, Martin Ignacio
Masty?o, M
Muro, Luis Santiago Miguel
author2_role author
author
author
author
dc.subject.none.fl_str_mv Projection constants
Boolean functions
local theory of Banach spaces
topic Projection constants
Boolean functions
local theory of Banach 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 The main aim of this work is to study important local Banach space constants for Boolean cube function spaces. Specifically, we focus on mathcal{B}_{mathcal{S}}^{N}, the finite-dimensional Banach space of all real-valued functions defined on the N-dimensional Boolean cube {-1, +1}^{N} that have Fourier–Walsh expansions supported on a fixed family of subsets of {1, ldots , N}⁠. Our investigation centers on the projection, Sidon, and Gordon–Lewis constants of this function space. We combine tools from different areas to derive exact formulas and asymptotic estimates of these parameters for special types of families depending on the dimension of the Boolean cube and other complexity characteristics of the support set ⁠. Using local Banach space theory, we establish the intimate relationship among these three important constants.
Fil: Defant, A.. Carl von Ossietzky Universität; Alemania
Fil: Galicer, Daniel Eric. 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: Mansilla, Martin Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Masty?o, M. Adam Mickiewicz University; Polonia
Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
description The main aim of this work is to study important local Banach space constants for Boolean cube function spaces. Specifically, we focus on mathcal{B}_{mathcal{S}}^{N}, the finite-dimensional Banach space of all real-valued functions defined on the N-dimensional Boolean cube {-1, +1}^{N} that have Fourier–Walsh expansions supported on a fixed family of subsets of {1, ldots , N}⁠. Our investigation centers on the projection, Sidon, and Gordon–Lewis constants of this function space. We combine tools from different areas to derive exact formulas and asymptotic estimates of these parameters for special types of families depending on the dimension of the Boolean cube and other complexity characteristics of the support set ⁠. Using local Banach space theory, we establish the intimate relationship among these three important constants.
publishDate 2024
dc.date.none.fl_str_mv 2024-08
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/11336/257790
Defant, A.; Galicer, Daniel Eric; Mansilla, Martin Ignacio; Masty?o, M; Muro, Luis Santiago Miguel; Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces; Oxford University Press; International Mathematics Research Notices; 2024; 15; 8-2024; 11239-11270
1073-7928
CONICET Digital
CONICET
url http://hdl.handle.net/11336/257790
identifier_str_mv Defant, A.; Galicer, Daniel Eric; Mansilla, Martin Ignacio; Masty?o, M; Muro, Luis Santiago Miguel; Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces; Oxford University Press; International Mathematics Research Notices; 2024; 15; 8-2024; 11239-11270
1073-7928
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://academic.oup.com/imrn/article/2024/15/11239/7687880
info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnae083
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 Oxford University Press
publisher.none.fl_str_mv Oxford 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 13.070432

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