Dynamics of non-convolution operators and holomorphy types

Autores
Muro, Luis Santiago Miguel; Pinasco, Damian; Savransky, Martin
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this article we study the hypercyclic behavior of non-convolution operators defined on spaces of analytic functions of different holomorphy types over Banach spaces. The operators in the family we analyze are a composition of differentiation and composition operators, and are extensions of operators in H(C) studied by Aron and Markose in 2004. The dynamics of this class of operators, in the context of one and several complex variables, was further investigated by many authors. It turns out that the situation is somewhat different and that some purely infinite dimensional difficulties appear. For example, in contrast to the several complex variable case, it may happen that the symbol of the composition operator has no fixed points and still, the operator is not hypercyclic. We also prove a Runge type theorem for holomorphy types on Banach spaces.
Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Pinasco, Damian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
Fil: Savransky, Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
COMPOSITION OPERATORS
DIFFERENTIATION OPERATORS
HOLOMORPHY TYPES
HYPERCYCLIC OPERATORS
NON-CONVOLUTION OPERATORS
STRONGLY MIXING OPERATORS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/98226
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/98226
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Dynamics of non-convolution operators and holomorphy typesMuro, Luis Santiago MiguelPinasco, DamianSavransky, MartinCOMPOSITION OPERATORSDIFFERENTIATION OPERATORSHOLOMORPHY TYPESHYPERCYCLIC OPERATORSNON-CONVOLUTION OPERATORSSTRONGLY MIXING OPERATORShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article we study the hypercyclic behavior of non-convolution operators defined on spaces of analytic functions of different holomorphy types over Banach spaces. The operators in the family we analyze are a composition of differentiation and composition operators, and are extensions of operators in H(C) studied by Aron and Markose in 2004. The dynamics of this class of operators, in the context of one and several complex variables, was further investigated by many authors. It turns out that the situation is somewhat different and that some purely infinite dimensional difficulties appear. For example, in contrast to the several complex variable case, it may happen that the symbol of the composition operator has no fixed points and still, the operator is not hypercyclic. We also prove a Runge type theorem for holomorphy types on Banach spaces.Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Pinasco, Damian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; ArgentinaFil: Savransky, Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaAcademic Press Inc Elsevier Science2018-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/98226Muro, Luis Santiago Miguel; Pinasco, Damian; Savransky, Martin; Dynamics of non-convolution operators and holomorphy types; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 468; 2; 12-2018; 622-6410022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2018.08.017info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022247X18306814info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:23:46Zoai:ri.conicet.gov.ar:11336/98226instacron: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:34982025-10-15 15:23:46.309CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Dynamics of non-convolution operators and holomorphy types
title Dynamics of non-convolution operators and holomorphy types
spellingShingle Dynamics of non-convolution operators and holomorphy types
Muro, Luis Santiago Miguel
COMPOSITION OPERATORS
DIFFERENTIATION OPERATORS
HOLOMORPHY TYPES
HYPERCYCLIC OPERATORS
NON-CONVOLUTION OPERATORS
STRONGLY MIXING OPERATORS
title_short Dynamics of non-convolution operators and holomorphy types
title_full Dynamics of non-convolution operators and holomorphy types
title_fullStr Dynamics of non-convolution operators and holomorphy types
title_full_unstemmed Dynamics of non-convolution operators and holomorphy types
title_sort Dynamics of non-convolution operators and holomorphy types
dc.creator.none.fl_str_mv Muro, Luis Santiago Miguel
Pinasco, Damian
Savransky, Martin
author Muro, Luis Santiago Miguel
author_facet Muro, Luis Santiago Miguel
Pinasco, Damian
Savransky, Martin
author_role author
author2 Pinasco, Damian
Savransky, Martin
author2_role author
author
dc.subject.none.fl_str_mv COMPOSITION OPERATORS
DIFFERENTIATION OPERATORS
HOLOMORPHY TYPES
HYPERCYCLIC OPERATORS
NON-CONVOLUTION OPERATORS
STRONGLY MIXING OPERATORS
topic COMPOSITION OPERATORS
DIFFERENTIATION OPERATORS
HOLOMORPHY TYPES
HYPERCYCLIC OPERATORS
NON-CONVOLUTION OPERATORS
STRONGLY MIXING OPERATORS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this article we study the hypercyclic behavior of non-convolution operators defined on spaces of analytic functions of different holomorphy types over Banach spaces. The operators in the family we analyze are a composition of differentiation and composition operators, and are extensions of operators in H(C) studied by Aron and Markose in 2004. The dynamics of this class of operators, in the context of one and several complex variables, was further investigated by many authors. It turns out that the situation is somewhat different and that some purely infinite dimensional difficulties appear. For example, in contrast to the several complex variable case, it may happen that the symbol of the composition operator has no fixed points and still, the operator is not hypercyclic. We also prove a Runge type theorem for holomorphy types on Banach spaces.
Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Pinasco, Damian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
Fil: Savransky, Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description In this article we study the hypercyclic behavior of non-convolution operators defined on spaces of analytic functions of different holomorphy types over Banach spaces. The operators in the family we analyze are a composition of differentiation and composition operators, and are extensions of operators in H(C) studied by Aron and Markose in 2004. The dynamics of this class of operators, in the context of one and several complex variables, was further investigated by many authors. It turns out that the situation is somewhat different and that some purely infinite dimensional difficulties appear. For example, in contrast to the several complex variable case, it may happen that the symbol of the composition operator has no fixed points and still, the operator is not hypercyclic. We also prove a Runge type theorem for holomorphy types on Banach spaces.
publishDate 2018
dc.date.none.fl_str_mv 2018-12
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/11336/98226
Muro, Luis Santiago Miguel; Pinasco, Damian; Savransky, Martin; Dynamics of non-convolution operators and holomorphy types; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 468; 2; 12-2018; 622-641
0022-247X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/98226
identifier_str_mv Muro, Luis Santiago Miguel; Pinasco, Damian; Savransky, Martin; Dynamics of non-convolution operators and holomorphy types; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 468; 2; 12-2018; 622-641
0022-247X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2018.08.017
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022247X18306814
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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
_version_ 1846083384727568384
score 13.216834

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