Hypercyclic homogeneous polynomials on H(C)

Autores
Cardeccia, Rodrigo Alejandro; Muro, Luis Santiago Miguel
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fréchet spaces. We show the existence of hypercyclic polynomials on H(C), by exhibiting a concrete polynomial which is also the first example of a frequently hypercyclic homogeneous polynomial on any F-space. We prove that the homogeneous polynomial on H(C) defined as the product of a translation operator and the evaluation at 0 is mixing, frequently hypercyclic and chaotic. We prove, in contrast, that some natural related polynomials fail to be hypercyclic.
Fil: Cardeccia, Rodrigo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentina
Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Materia
ENTIRE FUNCTIONS
FREQUENTLY HYPERCYCLIC OPERATORS
HOMOGENEOUS POLYNOMIALS
UNIVERSAL FUNCTIONS
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:11336/93951
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Hypercyclic homogeneous polynomials on H(C)Cardeccia, Rodrigo AlejandroMuro, Luis Santiago MiguelENTIRE FUNCTIONSFREQUENTLY HYPERCYCLIC OPERATORSHOMOGENEOUS POLYNOMIALSUNIVERSAL FUNCTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fréchet spaces. We show the existence of hypercyclic polynomials on H(C), by exhibiting a concrete polynomial which is also the first example of a frequently hypercyclic homogeneous polynomial on any F-space. We prove that the homogeneous polynomial on H(C) defined as the product of a translation operator and the evaluation at 0 is mixing, frequently hypercyclic and chaotic. We prove, in contrast, that some natural related polynomials fail to be hypercyclic.Fil: Cardeccia, Rodrigo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; ArgentinaFil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaAcademic Press Inc Elsevier Science2018-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/93951Cardeccia, Rodrigo Alejandro; Muro, Luis Santiago Miguel; Hypercyclic homogeneous polynomials on H(C); Academic Press Inc Elsevier Science; Journal Of Approximation Theory; 226; 2-2018; 60-720021-9045CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jat.2017.09.005info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021904517301193info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1703.04773info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:48:41Zoai:ri.conicet.gov.ar:11336/93951instacron: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 09:48:42.214CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Hypercyclic homogeneous polynomials on H(C)
title Hypercyclic homogeneous polynomials on H(C)
spellingShingle Hypercyclic homogeneous polynomials on H(C)
Cardeccia, Rodrigo Alejandro
ENTIRE FUNCTIONS
FREQUENTLY HYPERCYCLIC OPERATORS
HOMOGENEOUS POLYNOMIALS
UNIVERSAL FUNCTIONS
title_short Hypercyclic homogeneous polynomials on H(C)
title_full Hypercyclic homogeneous polynomials on H(C)
title_fullStr Hypercyclic homogeneous polynomials on H(C)
title_full_unstemmed Hypercyclic homogeneous polynomials on H(C)
title_sort Hypercyclic homogeneous polynomials on H(C)
dc.creator.none.fl_str_mv Cardeccia, Rodrigo Alejandro
Muro, Luis Santiago Miguel
author Cardeccia, Rodrigo Alejandro
author_facet Cardeccia, Rodrigo Alejandro
Muro, Luis Santiago Miguel
author_role author
author2 Muro, Luis Santiago Miguel
author2_role author
dc.subject.none.fl_str_mv ENTIRE FUNCTIONS
FREQUENTLY HYPERCYCLIC OPERATORS
HOMOGENEOUS POLYNOMIALS
UNIVERSAL FUNCTIONS
topic ENTIRE FUNCTIONS
FREQUENTLY HYPERCYCLIC OPERATORS
HOMOGENEOUS POLYNOMIALS
UNIVERSAL FUNCTIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fréchet spaces. We show the existence of hypercyclic polynomials on H(C), by exhibiting a concrete polynomial which is also the first example of a frequently hypercyclic homogeneous polynomial on any F-space. We prove that the homogeneous polynomial on H(C) defined as the product of a translation operator and the evaluation at 0 is mixing, frequently hypercyclic and chaotic. We prove, in contrast, that some natural related polynomials fail to be hypercyclic.
Fil: Cardeccia, Rodrigo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentina
Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
description It is known that homogeneous polynomials on Banach spaces cannot be hypercyclic, but there are examples of hypercyclic homogeneous polynomials on some non-normable Fréchet spaces. We show the existence of hypercyclic polynomials on H(C), by exhibiting a concrete polynomial which is also the first example of a frequently hypercyclic homogeneous polynomial on any F-space. We prove that the homogeneous polynomial on H(C) defined as the product of a translation operator and the evaluation at 0 is mixing, frequently hypercyclic and chaotic. We prove, in contrast, that some natural related polynomials fail to be hypercyclic.
publishDate 2018
dc.date.none.fl_str_mv 2018-02
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/11336/93951
Cardeccia, Rodrigo Alejandro; Muro, Luis Santiago Miguel; Hypercyclic homogeneous polynomials on H(C); Academic Press Inc Elsevier Science; Journal Of Approximation Theory; 226; 2-2018; 60-72
0021-9045
CONICET Digital
CONICET
url http://hdl.handle.net/11336/93951
identifier_str_mv Cardeccia, Rodrigo Alejandro; Muro, Luis Santiago Miguel; Hypercyclic homogeneous polynomials on H(C); Academic Press Inc Elsevier Science; Journal Of Approximation Theory; 226; 2-2018; 60-72
0021-9045
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.jat.2017.09.005
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021904517301193
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1703.04773
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
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score 13.070432

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