Spectrum of composition operators on S(R) with polynomial symbols

[EN] We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum reduces to {0}, while the spectrum of any non mean ergodic co...

Full description

Bibliographic Details
Authors: Fernández, Carmen, Galbis, Antonio, Jorda Mora, Enrique|||0000-0003-2980-1699
Format: article
Publication Date:2020
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/166135
Online Access:https://riunet.upv.es/handle/10251/166135
Access Level:Open access
Keyword:Composition operator
Space of rapidly decreasing functions
Spectrum
Mean ergodic operator
MATEMATICA APLICADA
id ES_cfcd76f57f646cbc9c8edf9fad4a83e9
oai_identifier_str oai:riunet.upv.es:10251/166135
network_acronym_str ES
network_name_str España
repository_id_str
spelling Spectrum of composition operators on S(R) with polynomial symbolsFernández, CarmenGalbis, AntonioJorda Mora, Enrique|||0000-0003-2980-1699Composition operatorSpace of rapidly decreasing functionsSpectrumMean ergodic operatorMATEMATICA APLICADA[EN] We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum reduces to {0}, while the spectrum of any non mean ergodic composition operator with a polynomial always contains the closed unit disc except perhaps the origin. We obtain a complete description of the spectrum of the composition operator with a quadratic polynomial or a cubic polynomial with positive leading coefficient.The present research was partially supported by the projects MTM2016-76647-P and Prometeo2017/102 (Spain).ElsevierDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Politécnica Superior de AlcoyGeneralitat ValencianaMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20202020-05-13journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/166135reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2016-76647-P ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIAGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2017%2F102 ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1661352026-06-13T07:49:27Z
dc.title.none.fl_str_mv Spectrum of composition operators on S(R) with polynomial symbols
title Spectrum of composition operators on S(R) with polynomial symbols
spellingShingle Spectrum of composition operators on S(R) with polynomial symbols
Fernández, Carmen
Composition operator
Space of rapidly decreasing functions
Spectrum
Mean ergodic operator
MATEMATICA APLICADA
title_short Spectrum of composition operators on S(R) with polynomial symbols
title_full Spectrum of composition operators on S(R) with polynomial symbols
title_fullStr Spectrum of composition operators on S(R) with polynomial symbols
title_full_unstemmed Spectrum of composition operators on S(R) with polynomial symbols
title_sort Spectrum of composition operators on S(R) with polynomial symbols
dc.creator.none.fl_str_mv Fernández, Carmen
Galbis, Antonio
Jorda Mora, Enrique|||0000-0003-2980-1699
author Fernández, Carmen
author_facet Fernández, Carmen
Galbis, Antonio
Jorda Mora, Enrique|||0000-0003-2980-1699
author_role author
author2 Galbis, Antonio
Jorda Mora, Enrique|||0000-0003-2980-1699
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Pura y Aplicada
Escuela Politécnica Superior de Alcoy
Generalitat Valenciana
Ministerio de Economía y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Composition operator
Space of rapidly decreasing functions
Spectrum
Mean ergodic operator
MATEMATICA APLICADA
topic Composition operator
Space of rapidly decreasing functions
Spectrum
Mean ergodic operator
MATEMATICA APLICADA
description [EN] We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum reduces to {0}, while the spectrum of any non mean ergodic composition operator with a polynomial always contains the closed unit disc except perhaps the origin. We obtain a complete description of the spectrum of the composition operator with a quadratic polynomial or a cubic polynomial with positive leading coefficient.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-05-13
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/10251/166135
url https://riunet.upv.es/handle/10251/166135
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2016-76647-P ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIA
Generalitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2017%2F102 ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/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 - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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
_version_ 1869420116270120960
score 15,300719

Similar Items