Linear Kierst-Szpilrajn theorems

We prove in this paper the following result which extends in a somewhat ‘linear’ sense a theorem by Kierst and Szpilrajn and which holds on many ‘natural’ spaces of holomorphic functions in the open unit disk D: There exist a dense linear manifold and a closed infinite-dimensional linear manifold of...

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Autor: Bernal González, Luis
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2005
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/87529
Acceso en línea:https://hdl.handle.net/11441/87529
https://doi.org/10.4064/sm166-1-4
Access Level:acceso abierto
Palabra clave:Domain of holomorphy
Unit disk
Residual set
Dense linear manifold
Closed linear manifold
Ggap series
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spelling Linear Kierst-Szpilrajn theoremsBernal González, LuisDomain of holomorphyUnit diskResidual setDense linear manifoldClosed linear manifoldGgap seriesWe prove in this paper the following result which extends in a somewhat ‘linear’ sense a theorem by Kierst and Szpilrajn and which holds on many ‘natural’ spaces of holomorphic functions in the open unit disk D: There exist a dense linear manifold and a closed infinite-dimensional linear manifold of holomorphic functions in D whose domain of holomorphy is D except for the null function. The existence of a dense linear manifold of noncontinuable functions is also shown in any domain for its full space of holomorphic functions.Plan Andaluz de Investigación (Junta de Andalucía)Dirección General de Enseñanza Superior (DGES). EspañaPolish Academy of Sciences, Institute of MathematicsAnálisis MatemáticoFQM127: Análisis Funcional no Lineal2005info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/87529https://doi.org/10.4064/sm166-1-4reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésStudia Mathematica, 166, 55-69.FQM-127BFM2003-03893- C02-01https://www.impan.pl/shop/en/publication/transaction/download/product/90493info:eu-repo/semantics/openAccessoai:idus.us.es:11441/875292026-06-17T12:51:07Z
dc.title.none.fl_str_mv Linear Kierst-Szpilrajn theorems
title Linear Kierst-Szpilrajn theorems
spellingShingle Linear Kierst-Szpilrajn theorems
Bernal González, Luis
Domain of holomorphy
Unit disk
Residual set
Dense linear manifold
Closed linear manifold
Ggap series
title_short Linear Kierst-Szpilrajn theorems
title_full Linear Kierst-Szpilrajn theorems
title_fullStr Linear Kierst-Szpilrajn theorems
title_full_unstemmed Linear Kierst-Szpilrajn theorems
title_sort Linear Kierst-Szpilrajn theorems
dc.creator.none.fl_str_mv Bernal González, Luis
author Bernal González, Luis
author_facet Bernal González, Luis
author_role author
dc.contributor.none.fl_str_mv Análisis Matemático
FQM127: Análisis Funcional no Lineal
dc.subject.none.fl_str_mv Domain of holomorphy
Unit disk
Residual set
Dense linear manifold
Closed linear manifold
Ggap series
topic Domain of holomorphy
Unit disk
Residual set
Dense linear manifold
Closed linear manifold
Ggap series
description We prove in this paper the following result which extends in a somewhat ‘linear’ sense a theorem by Kierst and Szpilrajn and which holds on many ‘natural’ spaces of holomorphic functions in the open unit disk D: There exist a dense linear manifold and a closed infinite-dimensional linear manifold of holomorphic functions in D whose domain of holomorphy is D except for the null function. The existence of a dense linear manifold of noncontinuable functions is also shown in any domain for its full space of holomorphic functions.
publishDate 2005
dc.date.none.fl_str_mv 2005
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/11441/87529
https://doi.org/10.4064/sm166-1-4
url https://hdl.handle.net/11441/87529
https://doi.org/10.4064/sm166-1-4
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Studia Mathematica, 166, 55-69.
FQM-127
BFM2003-03893- C02-01
https://www.impan.pl/shop/en/publication/transaction/download/product/90493
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 Polish Academy of Sciences, Institute of Mathematics
publisher.none.fl_str_mv Polish Academy of Sciences, Institute of Mathematics
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 15,300724

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