Dense-lineability of sets of Birkhoff-universal functions with rapid decay

Let A be an unbounded Arakelian set in the complex plane whose complement has infinite inscribed radius, and ψ be an increasing positive function on the positive real numbers. We prove the existence of a dense linear manifold M of entire functions all of whose nonzero members are Birkhoff-universal,...

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Autores: Bernal González, Luis, Calderón Moreno, María del Carmen, Luh, Wolfgang
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2010
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/87511
Acceso en línea:https://hdl.handle.net/11441/87511
https://doi.org/10.1016/j.jmaa.2009.08.049
Access Level:acceso abierto
Palabra clave:Birkhoff-universal function
Dense lineability
Arakelian set
Infinite order differential operator
Growth of entire functions
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spelling Dense-lineability of sets of Birkhoff-universal functions with rapid decayBernal González, LuisCalderón Moreno, María del CarmenLuh, WolfgangBirkhoff-universal functionDense lineabilityArakelian setInfinite order differential operatorGrowth of entire functionsLet A be an unbounded Arakelian set in the complex plane whose complement has infinite inscribed radius, and ψ be an increasing positive function on the positive real numbers. We prove the existence of a dense linear manifold M of entire functions all of whose nonzero members are Birkhoff-universal, such that each function in M has overall growth faster than ψ and, in addition, exp(|z|α)f(z) → 0 (z → ∞, z ∈ A) for all α < 1/2 and f ∈ M. With slightly more restrictive conditions on A, we get that the last property also holds for the action T f of certain holomorphic operators T. Our results unify, extend and complete recent work by several authors.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Educación y Ciencia (MEC). EspañaElsevierAnálisis MatemáticoFQM127: Análisis Funcional no Lineal2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/87511https://doi.org/10.1016/j.jmaa.2009.08.049reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Mathematical Analysis and Applications, 363 (1), 327-335.FQM-127MTM2006-13997-C02-01MTM2006-26627-Ehttps://reader.elsevier.com/reader/sd/pii/S0022247X09006921?token=F06CBABEA29041F303D8C566E85BD689976E8DD996934ECA5619EB9453EDCEFAD67467141FD80BE03419D304DC8C547Ainfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/875112026-06-17T12:51:07Z
dc.title.none.fl_str_mv Dense-lineability of sets of Birkhoff-universal functions with rapid decay
title Dense-lineability of sets of Birkhoff-universal functions with rapid decay
spellingShingle Dense-lineability of sets of Birkhoff-universal functions with rapid decay
Bernal González, Luis
Birkhoff-universal function
Dense lineability
Arakelian set
Infinite order differential operator
Growth of entire functions
title_short Dense-lineability of sets of Birkhoff-universal functions with rapid decay
title_full Dense-lineability of sets of Birkhoff-universal functions with rapid decay
title_fullStr Dense-lineability of sets of Birkhoff-universal functions with rapid decay
title_full_unstemmed Dense-lineability of sets of Birkhoff-universal functions with rapid decay
title_sort Dense-lineability of sets of Birkhoff-universal functions with rapid decay
dc.creator.none.fl_str_mv Bernal González, Luis
Calderón Moreno, María del Carmen
Luh, Wolfgang
author Bernal González, Luis
author_facet Bernal González, Luis
Calderón Moreno, María del Carmen
Luh, Wolfgang
author_role author
author2 Calderón Moreno, María del Carmen
Luh, Wolfgang
author2_role author
author
dc.contributor.none.fl_str_mv Análisis Matemático
FQM127: Análisis Funcional no Lineal
dc.subject.none.fl_str_mv Birkhoff-universal function
Dense lineability
Arakelian set
Infinite order differential operator
Growth of entire functions
topic Birkhoff-universal function
Dense lineability
Arakelian set
Infinite order differential operator
Growth of entire functions
description Let A be an unbounded Arakelian set in the complex plane whose complement has infinite inscribed radius, and ψ be an increasing positive function on the positive real numbers. We prove the existence of a dense linear manifold M of entire functions all of whose nonzero members are Birkhoff-universal, such that each function in M has overall growth faster than ψ and, in addition, exp(|z|α)f(z) → 0 (z → ∞, z ∈ A) for all α < 1/2 and f ∈ M. With slightly more restrictive conditions on A, we get that the last property also holds for the action T f of certain holomorphic operators T. Our results unify, extend and complete recent work by several authors.
publishDate 2010
dc.date.none.fl_str_mv 2010
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/87511
https://doi.org/10.1016/j.jmaa.2009.08.049
url https://hdl.handle.net/11441/87511
https://doi.org/10.1016/j.jmaa.2009.08.049
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Mathematical Analysis and Applications, 363 (1), 327-335.
FQM-127
MTM2006-13997-C02-01
MTM2006-26627-E
https://reader.elsevier.com/reader/sd/pii/S0022247X09006921?token=F06CBABEA29041F303D8C566E85BD689976E8DD996934ECA5619EB9453EDCEFAD67467141FD80BE03419D304DC8C547A
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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