Power boundedness and related properties for weighted composition operators on S(R)

[EN] We characterize those pairs of smooth mappings for which the corresponding weighted composition operator acts continuously on . Additionally, we give several easy-to-check necessary and sufficient conditions of this property for interesting special cases. Moreover, we characterize power bounded...

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Autores: Asensio López, Vicente|||0000-0002-7615-4140, Jorda Mora, Enrique|||0000-0003-2980-1699, Kalmes, Thomas
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/213118
Acceso en línea:https://riunet.upv.es/handle/10251/213118
Access Level:acceso abierto
Palabra clave:Weighted composition operator
Power bounded operator
Mean ergodic operator
Space of rapidly decreasing smooth functions
MATEMATICA APLICADA
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spelling Power boundedness and related properties for weighted composition operators on S(R)Asensio López, Vicente|||0000-0002-7615-4140Jorda Mora, Enrique|||0000-0003-2980-1699Kalmes, ThomasWeighted composition operatorPower bounded operatorMean ergodic operatorSpace of rapidly decreasing smooth functionsMATEMATICA APLICADA[EN] We characterize those pairs of smooth mappings for which the corresponding weighted composition operator acts continuously on . Additionally, we give several easy-to-check necessary and sufficient conditions of this property for interesting special cases. Moreover, we characterize power boundedness and topologizablity of on in terms of . Among other things, as an application of our results we show that for a univariate polynomial ¿ with , power boundedness of on for every only depends on ¿ and that in this case power boundedness of is equivalent to converging to 0 in as well as to the uniform mean ergodicity of . Additionally, we give an example of a power bounded and uniformly mean ergodic weighted composition operator on for which neither the multiplication operator nor the composition operator acts on . Our results complement and considerably extend various results of Fernández, Galbis, and the second named author.The research on the topic of this article was initiated during a visit of the third named author at Departamento de Matemática Aplicada, E. Politécnica Superior de Alcoy, Universidad Politécnica de Valencia. He is very grateful to his colleagues from Valencia for the cordial hospitality during this stay as well as during numerous earlier ones. The first named author was supported by GV PROMETEU/2021/070. The second and third named authors were partially supported by the project PID2020-119457GB-100 funded by MCIN/AEI/10.13039/501100011033 and ERDF A way of making Europe .ElsevierDepartamento de Matemática AplicadaEscuela Técnica Superior de ArquitecturaInstituto Universitario de Matemática Pura y AplicadaEscuela Politécnica Superior de AlcoyEscuela Técnica Superior de Ingeniería InformáticaGENERALITAT VALENCIANAAGENCIA ESTATAL DE INVESTIGACIONEuropean Regional Development FundRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-02-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/213118reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-119457GB-I00 METODOS DEL ANALISIS FUNCIONAL PARA LA TEORIA DE OPERADORES Y EL ANALISIS TIEMPO-FRECUENCIAGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2021%2F070 Análisis funcional, dinámica de operadores y aplicacionesopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2131182026-06-13T07:49:27Z
dc.title.none.fl_str_mv Power boundedness and related properties for weighted composition operators on S(R)
title Power boundedness and related properties for weighted composition operators on S(R)
spellingShingle Power boundedness and related properties for weighted composition operators on S(R)
Asensio López, Vicente|||0000-0002-7615-4140
Weighted composition operator
Power bounded operator
Mean ergodic operator
Space of rapidly decreasing smooth functions
MATEMATICA APLICADA
title_short Power boundedness and related properties for weighted composition operators on S(R)
title_full Power boundedness and related properties for weighted composition operators on S(R)
title_fullStr Power boundedness and related properties for weighted composition operators on S(R)
title_full_unstemmed Power boundedness and related properties for weighted composition operators on S(R)
title_sort Power boundedness and related properties for weighted composition operators on S(R)
dc.creator.none.fl_str_mv Asensio López, Vicente|||0000-0002-7615-4140
Jorda Mora, Enrique|||0000-0003-2980-1699
Kalmes, Thomas
author Asensio López, Vicente|||0000-0002-7615-4140
author_facet Asensio López, Vicente|||0000-0002-7615-4140
Jorda Mora, Enrique|||0000-0003-2980-1699
Kalmes, Thomas
author_role author
author2 Jorda Mora, Enrique|||0000-0003-2980-1699
Kalmes, Thomas
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Arquitectura
Instituto Universitario de Matemática Pura y Aplicada
Escuela Politécnica Superior de Alcoy
Escuela Técnica Superior de Ingeniería Informática
GENERALITAT VALENCIANA
AGENCIA ESTATAL DE INVESTIGACION
European Regional Development Fund
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Weighted composition operator
Power bounded operator
Mean ergodic operator
Space of rapidly decreasing smooth functions
MATEMATICA APLICADA
topic Weighted composition operator
Power bounded operator
Mean ergodic operator
Space of rapidly decreasing smooth functions
MATEMATICA APLICADA
description [EN] We characterize those pairs of smooth mappings for which the corresponding weighted composition operator acts continuously on . Additionally, we give several easy-to-check necessary and sufficient conditions of this property for interesting special cases. Moreover, we characterize power boundedness and topologizablity of on in terms of . Among other things, as an application of our results we show that for a univariate polynomial ¿ with , power boundedness of on for every only depends on ¿ and that in this case power boundedness of is equivalent to converging to 0 in as well as to the uniform mean ergodicity of . Additionally, we give an example of a power bounded and uniformly mean ergodic weighted composition operator on for which neither the multiplication operator nor the composition operator acts on . Our results complement and considerably extend various results of Fernández, Galbis, and the second named author.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-02-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
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 https://riunet.upv.es/handle/10251/213118
url https://riunet.upv.es/handle/10251/213118
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-119457GB-I00 METODOS DEL ANALISIS FUNCIONAL PARA LA TEORIA DE OPERADORES Y EL ANALISIS TIEMPO-FRECUENCIA
Generalitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2021%2F070 Análisis funcional, dinámica de operadores y aplicaciones
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
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
Reconocimiento (by)
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 Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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