Pseudo-Fubini Real-Entire Functions on the Plane

In this note, it is proved the existence of a c -dimensional vector space of real-entire functions all of whose nonzero members are non-integrable in the sense of Lebesgue but yet their two iterated integrals exist as real numbers and coincide. Moreover, it is shown that this vector space can be cho...

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Autores: Bernal González, Luis, Calderón Moreno, María del Carmen, Jung, Andreas
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/144838
Acceso en línea:https://hdl.handle.net/11441/144838
https://doi.org/10.1007/s00009-022-02149-5
Access Level:acceso abierto
Palabra clave:Fubini’s theorem
real entire functions
iterated integrals
dense lineability
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spelling Pseudo-Fubini Real-Entire Functions on the PlaneBernal González, LuisCalderón Moreno, María del CarmenJung, AndreasFubini’s theoremreal entire functionsiterated integralsdense lineabilityIn this note, it is proved the existence of a c -dimensional vector space of real-entire functions all of whose nonzero members are non-integrable in the sense of Lebesgue but yet their two iterated integrals exist as real numbers and coincide. Moreover, it is shown that this vector space can be chosen to be dense in the space of all real C∞ -functions on the plane endowed with the topology of uniform convergence on compacta for all derivatives of all orders. If the condition of being entire is dropped, then a closed infinite dimensional subspace satisfying the same properties can be obtained.SpringerAnálisis Matemático2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/144838https://doi.org/10.1007/s00009-022-02149-5reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMEDITERRANEAN JOURNAL OF MATHEMATICS ( / ), 19 (5), 218-1.https://doi.org/10.1007/s00009-022-02149-5info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1448382026-06-17T12:51:07Z
dc.title.none.fl_str_mv Pseudo-Fubini Real-Entire Functions on the Plane
title Pseudo-Fubini Real-Entire Functions on the Plane
spellingShingle Pseudo-Fubini Real-Entire Functions on the Plane
Bernal González, Luis
Fubini’s theorem
real entire functions
iterated integrals
dense lineability
title_short Pseudo-Fubini Real-Entire Functions on the Plane
title_full Pseudo-Fubini Real-Entire Functions on the Plane
title_fullStr Pseudo-Fubini Real-Entire Functions on the Plane
title_full_unstemmed Pseudo-Fubini Real-Entire Functions on the Plane
title_sort Pseudo-Fubini Real-Entire Functions on the Plane
dc.creator.none.fl_str_mv Bernal González, Luis
Calderón Moreno, María del Carmen
Jung, Andreas
author Bernal González, Luis
author_facet Bernal González, Luis
Calderón Moreno, María del Carmen
Jung, Andreas
author_role author
author2 Calderón Moreno, María del Carmen
Jung, Andreas
author2_role author
author
dc.contributor.none.fl_str_mv Análisis Matemático
dc.subject.none.fl_str_mv Fubini’s theorem
real entire functions
iterated integrals
dense lineability
topic Fubini’s theorem
real entire functions
iterated integrals
dense lineability
description In this note, it is proved the existence of a c -dimensional vector space of real-entire functions all of whose nonzero members are non-integrable in the sense of Lebesgue but yet their two iterated integrals exist as real numbers and coincide. Moreover, it is shown that this vector space can be chosen to be dense in the space of all real C∞ -functions on the plane endowed with the topology of uniform convergence on compacta for all derivatives of all orders. If the condition of being entire is dropped, then a closed infinite dimensional subspace satisfying the same properties can be obtained.
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/144838
https://doi.org/10.1007/s00009-022-02149-5
url https://hdl.handle.net/11441/144838
https://doi.org/10.1007/s00009-022-02149-5
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv MEDITERRANEAN JOURNAL OF MATHEMATICS ( / ), 19 (5), 218-1.
https://doi.org/10.1007/s00009-022-02149-5
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 Springer
publisher.none.fl_str_mv Springer
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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score 15,300719

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