Representations by Beurling Systems

We prove that a Beurling system with (Formula presented.) is an (Formula presented.) —basis in (Formula presented.) with an explicit dual system. Any function (Formula presented.) can be expanded as a series by the system (Formula presented.) For different summation methods, we characterize the oute...

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Detalles Bibliográficos
Autor: Ghazaryan, Ghazaros
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/714383
Acceso en línea:http://hdl.handle.net/10486/714383
https://dx.doi.org/10.3390/math11173663
Access Level:acceso abierto
Palabra clave:Beurling system
hardy spaces
kernels
outer function
representation of functions
summation basis
Matemáticas
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spelling Representations by Beurling SystemsGhazaryan, GhazarosBeurling systemhardy spaceskernelsouter functionrepresentation of functionssummation basisMatemáticasWe prove that a Beurling system with (Formula presented.) is an (Formula presented.) —basis in (Formula presented.) with an explicit dual system. Any function (Formula presented.) can be expanded as a series by the system (Formula presented.) For different summation methods, we characterize the outer functions F for which the expansion with respect to the corresponding Beurling system converges to f. Related results for weighted Hardy spaces in the unit disc are studied. Particularly we prove Rosenblum’s hypothesisThis research received no external fundingMultidisciplinary Digital Publishing Institute (MDPI)Departamento de MatemáticasFacultad de Ciencias20232023-08-24research articlehttp://purl.org/coar/resource_type/c_2df8fbb1VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/714383https://dx.doi.org/10.3390/math11173663reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7143832026-06-23T12:46:27Z
dc.title.none.fl_str_mv Representations by Beurling Systems
title Representations by Beurling Systems
spellingShingle Representations by Beurling Systems
Ghazaryan, Ghazaros
Beurling system
hardy spaces
kernels
outer function
representation of functions
summation basis
Matemáticas
title_short Representations by Beurling Systems
title_full Representations by Beurling Systems
title_fullStr Representations by Beurling Systems
title_full_unstemmed Representations by Beurling Systems
title_sort Representations by Beurling Systems
dc.creator.none.fl_str_mv Ghazaryan, Ghazaros
author Ghazaryan, Ghazaros
author_facet Ghazaryan, Ghazaros
author_role author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Beurling system
hardy spaces
kernels
outer function
representation of functions
summation basis
Matemáticas
topic Beurling system
hardy spaces
kernels
outer function
representation of functions
summation basis
Matemáticas
description We prove that a Beurling system with (Formula presented.) is an (Formula presented.) —basis in (Formula presented.) with an explicit dual system. Any function (Formula presented.) can be expanded as a series by the system (Formula presented.) For different summation methods, we characterize the outer functions F for which the expansion with respect to the corresponding Beurling system converges to f. Related results for weighted Hardy spaces in the unit disc are studied. Particularly we prove Rosenblum’s hypothesis
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-08-24
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/714383
https://dx.doi.org/10.3390/math11173663
url http://hdl.handle.net/10486/714383
https://dx.doi.org/10.3390/math11173663
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute (MDPI)
publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute (MDPI)
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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