A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions

Autores
Fernández Vidal, Tomás Ariel; Galicer, Daniel Eric; Sevilla Peris, Pablo
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give a version of the Montel theorem for Hardy spaces of holomorphic functions on an infinite dimensional space. Precisely, we show that any bounded sequence of holomorphic functions in some Hardy space, has a subsequence that converges uniformly over compact subsets to a function that also belongs to the same Hardy space. As a by-product of our results for spaces of functions on infinitely many variables, we also provide an elementary proof of a Montel-type theorem for the Hardy space of Dirichlet series.
Fil: Fernández Vidal, Tomás Ariel. 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: 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: Sevilla Peris, Pablo. Universidad Politécnica de Valencia; España
Materia
HARDY SPACES
INFINITE DIMENSIONAL ANALYSIS
MONTEL THEOREM
SPACES OF DIRICHLET SERIES
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:11336/214387
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A Montel-Type Theorem for Hardy Spaces of Holomorphic FunctionsFernández Vidal, Tomás ArielGalicer, Daniel EricSevilla Peris, PabloHARDY SPACESINFINITE DIMENSIONAL ANALYSISMONTEL THEOREMSPACES OF DIRICHLET SERIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give a version of the Montel theorem for Hardy spaces of holomorphic functions on an infinite dimensional space. Precisely, we show that any bounded sequence of holomorphic functions in some Hardy space, has a subsequence that converges uniformly over compact subsets to a function that also belongs to the same Hardy space. As a by-product of our results for spaces of functions on infinitely many variables, we also provide an elementary proof of a Montel-type theorem for the Hardy space of Dirichlet series.Fil: Fernández Vidal, Tomás Ariel. 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: 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: Sevilla Peris, Pablo. Universidad Politécnica de Valencia; EspañaBirkhauser Verlag Ag2022-08info: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/11336/214387Fernández Vidal, Tomás Ariel; Galicer, Daniel Eric; Sevilla Peris, Pablo; A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions; Birkhauser Verlag Ag; Mediterranean Journal Of Mathematics; 19; 5; 8-2022; 1-131660-5446CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/10.1007/s00009-022-02110-6info:eu-repo/semantics/altIdentifier/doi/10.1007/s00009-022-02110-6info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:39:10Zoai:ri.conicet.gov.ar:11336/214387instacron: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 09:39:10.465CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions
title A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions
spellingShingle A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions
Fernández Vidal, Tomás Ariel
HARDY SPACES
INFINITE DIMENSIONAL ANALYSIS
MONTEL THEOREM
SPACES OF DIRICHLET SERIES
title_short A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions
title_full A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions
title_fullStr A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions
title_full_unstemmed A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions
title_sort A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions
dc.creator.none.fl_str_mv Fernández Vidal, Tomás Ariel
Galicer, Daniel Eric
Sevilla Peris, Pablo
author Fernández Vidal, Tomás Ariel
author_facet Fernández Vidal, Tomás Ariel
Galicer, Daniel Eric
Sevilla Peris, Pablo
author_role author
author2 Galicer, Daniel Eric
Sevilla Peris, Pablo
author2_role author
author
dc.subject.none.fl_str_mv HARDY SPACES
INFINITE DIMENSIONAL ANALYSIS
MONTEL THEOREM
SPACES OF DIRICHLET SERIES
topic HARDY SPACES
INFINITE DIMENSIONAL ANALYSIS
MONTEL THEOREM
SPACES OF DIRICHLET SERIES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We give a version of the Montel theorem for Hardy spaces of holomorphic functions on an infinite dimensional space. Precisely, we show that any bounded sequence of holomorphic functions in some Hardy space, has a subsequence that converges uniformly over compact subsets to a function that also belongs to the same Hardy space. As a by-product of our results for spaces of functions on infinitely many variables, we also provide an elementary proof of a Montel-type theorem for the Hardy space of Dirichlet series.
Fil: Fernández Vidal, Tomás Ariel. 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: 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: Sevilla Peris, Pablo. Universidad Politécnica de Valencia; España
description We give a version of the Montel theorem for Hardy spaces of holomorphic functions on an infinite dimensional space. Precisely, we show that any bounded sequence of holomorphic functions in some Hardy space, has a subsequence that converges uniformly over compact subsets to a function that also belongs to the same Hardy space. As a by-product of our results for spaces of functions on infinitely many variables, we also provide an elementary proof of a Montel-type theorem for the Hardy space of Dirichlet series.
publishDate 2022
dc.date.none.fl_str_mv 2022-08
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/11336/214387
Fernández Vidal, Tomás Ariel; Galicer, Daniel Eric; Sevilla Peris, Pablo; A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions; Birkhauser Verlag Ag; Mediterranean Journal Of Mathematics; 19; 5; 8-2022; 1-13
1660-5446
CONICET Digital
CONICET
url http://hdl.handle.net/11336/214387
identifier_str_mv Fernández Vidal, Tomás Ariel; Galicer, Daniel Eric; Sevilla Peris, Pablo; A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions; Birkhauser Verlag Ag; Mediterranean Journal Of Mathematics; 19; 5; 8-2022; 1-13
1660-5446
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/s00009-022-02110-6
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00009-022-02110-6
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 Birkhauser Verlag Ag
publisher.none.fl_str_mv Birkhauser Verlag Ag
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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