Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions

Autores
Muro, Luis Santiago Miguel; Pinasco, Damian; Savransky, Martin
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on (Formula Presented.) are hypercyclic. Moreover, it was shown by Bonilla and Grosse-Erdmann that they have frequently hypercyclic functions of exponential growth. On the other hand, in the infinite dimensional setting, the Godefroy–Shapiro theorem has been extended to several spaces of entire functions defined on Banach spaces. We prove that on all these spaces, non-trivial convolution operators are strongly mixing with respect to a gaussian probability measure of full support. For the proof we combine the results previously mentioned and we use techniques recently developed by Bayart and Matheron. We also obtain the existence of frequently hypercyclic entire functions of exponential growth.
Fil: Muro, Luis Santiago Miguel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Pinasco, Damian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Savransky, Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
CONVOLUTION OPERATORS
FREQUENTLY HYPERCYCLIC OPERATORS
HOLOMORPHY TYPES
STRONGLY MIXING OPERATORS
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:11336/84445
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic FunctionsMuro, Luis Santiago MiguelPinasco, DamianSavransky, MartinCONVOLUTION OPERATORSFREQUENTLY HYPERCYCLIC OPERATORSHOLOMORPHY TYPESSTRONGLY MIXING OPERATORShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on (Formula Presented.) are hypercyclic. Moreover, it was shown by Bonilla and Grosse-Erdmann that they have frequently hypercyclic functions of exponential growth. On the other hand, in the infinite dimensional setting, the Godefroy–Shapiro theorem has been extended to several spaces of entire functions defined on Banach spaces. We prove that on all these spaces, non-trivial convolution operators are strongly mixing with respect to a gaussian probability measure of full support. For the proof we combine the results previously mentioned and we use techniques recently developed by Bayart and Matheron. We also obtain the existence of frequently hypercyclic entire functions of exponential growth.Fil: Muro, Luis Santiago Miguel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pinasco, Damian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Savransky, Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaBirkhauser Verlag Ag2014-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84445Muro, Luis Santiago Miguel; Pinasco, Damian; Savransky, Martin; Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 80; 4; 11-2014; 453-4680378-620X1420-8989CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s00020-014-2182-5info:eu-repo/semantics/altIdentifier/doi/10.1007/s00020-014-2182-5info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1311.7671info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:15:21Zoai:ri.conicet.gov.ar:11336/84445instacron: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 15:15:21.342CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
title Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
spellingShingle Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
Muro, Luis Santiago Miguel
CONVOLUTION OPERATORS
FREQUENTLY HYPERCYCLIC OPERATORS
HOLOMORPHY TYPES
STRONGLY MIXING OPERATORS
title_short Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
title_full Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
title_fullStr Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
title_full_unstemmed Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
title_sort Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions
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 CONVOLUTION OPERATORS
FREQUENTLY HYPERCYCLIC OPERATORS
HOLOMORPHY TYPES
STRONGLY MIXING OPERATORS
topic CONVOLUTION OPERATORS
FREQUENTLY HYPERCYCLIC OPERATORS
HOLOMORPHY TYPES
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 A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on (Formula Presented.) are hypercyclic. Moreover, it was shown by Bonilla and Grosse-Erdmann that they have frequently hypercyclic functions of exponential growth. On the other hand, in the infinite dimensional setting, the Godefroy–Shapiro theorem has been extended to several spaces of entire functions defined on Banach spaces. We prove that on all these spaces, non-trivial convolution operators are strongly mixing with respect to a gaussian probability measure of full support. For the proof we combine the results previously mentioned and we use techniques recently developed by Bayart and Matheron. We also obtain the existence of frequently hypercyclic entire functions of exponential growth.
Fil: Muro, Luis Santiago Miguel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Pinasco, Damian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Savransky, Martin. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description A theorem of Godefroy and Shapiro states that non-trivial convolution operators on the space of entire functions on (Formula Presented.) are hypercyclic. Moreover, it was shown by Bonilla and Grosse-Erdmann that they have frequently hypercyclic functions of exponential growth. On the other hand, in the infinite dimensional setting, the Godefroy–Shapiro theorem has been extended to several spaces of entire functions defined on Banach spaces. We prove that on all these spaces, non-trivial convolution operators are strongly mixing with respect to a gaussian probability measure of full support. For the proof we combine the results previously mentioned and we use techniques recently developed by Bayart and Matheron. We also obtain the existence of frequently hypercyclic entire functions of exponential growth.
publishDate 2014
dc.date.none.fl_str_mv 2014-11
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/11336/84445
Muro, Luis Santiago Miguel; Pinasco, Damian; Savransky, Martin; Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 80; 4; 11-2014; 453-468
0378-620X
1420-8989
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84445
identifier_str_mv Muro, Luis Santiago Miguel; Pinasco, Damian; Savransky, Martin; Strongly Mixing Convolution Operators on Fréchet Spaces of Holomorphic Functions; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 80; 4; 11-2014; 453-468
0378-620X
1420-8989
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s00020-014-2182-5
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00020-014-2182-5
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1311.7671
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
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
_version_ 1846083301476925440
score 13.219909

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