Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions

Answering a question of Lindholm, we prove strict density inequalities for sampling and interpolation in Fock spaces of entire functions in several complex variables defined by a plurisubharmonic weight. In particular, these spaces do not admit a set that is simultaneously sampling and interpolating...

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Detalles Bibliográficos
Autores: Gröchenig, Karlheinz, Haimi, Antti, Ortega Cerdà, Joaquim, Romero, José Luis
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/164420
Acceso en línea:https://hdl.handle.net/2445/164420
Access Level:acceso abierto
Palabra clave:Funcions enteres
Nuclis de Bergman
Funcions de diverses variables complexes
Anàlisi harmònica
Entire functions
Bergman kernel functions
Functions of several complex variables
Harmonic analysis
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spelling Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functionsGröchenig, KarlheinzHaimi, AnttiOrtega Cerdà, JoaquimRomero, José LuisFuncions enteresNuclis de BergmanFuncions de diverses variables complexesAnàlisi harmònicaEntire functionsBergman kernel functionsFunctions of several complex variablesHarmonic analysisAnswering a question of Lindholm, we prove strict density inequalities for sampling and interpolation in Fock spaces of entire functions in several complex variables defined by a plurisubharmonic weight. In particular, these spaces do not admit a set that is simultaneously sampling and interpolating. To prove optimality of the density conditions, we construct sampling sets with a density arbitrarily close to the critical density. The techniques combine methods from several complex variables (estimates for $\bar \partial$) and the theory of localized frames in general reproducing kernel Hilbert spaces (with no analyticity assumed). The abstract results on Fekete points and deformation of frames may be of independent interest.Elsevier2020202120192020info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/2445/164420Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió postprint del document publicat a: https://doi.org/10.1016/j.jfa.2019.108282Journal of Functional Analysis, 2019, vol. 277, num. 12https://doi.org/10.1016/j.jfa.2019.108282cc-by-nc-nd (c) Elsevier, 2019http://creativecommons.org/licenses/by-nc-nd/3.0/esinfo:eu-repo/semantics/openAccessoai:recercat.cat:2445/1644202026-05-29T05:05:01Z
dc.title.none.fl_str_mv Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
title Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
spellingShingle Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
Gröchenig, Karlheinz
Funcions enteres
Nuclis de Bergman
Funcions de diverses variables complexes
Anàlisi harmònica
Entire functions
Bergman kernel functions
Functions of several complex variables
Harmonic analysis
title_short Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
title_full Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
title_fullStr Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
title_full_unstemmed Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
title_sort Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
dc.creator.none.fl_str_mv Gröchenig, Karlheinz
Haimi, Antti
Ortega Cerdà, Joaquim
Romero, José Luis
author Gröchenig, Karlheinz
author_facet Gröchenig, Karlheinz
Haimi, Antti
Ortega Cerdà, Joaquim
Romero, José Luis
author_role author
author2 Haimi, Antti
Ortega Cerdà, Joaquim
Romero, José Luis
author2_role author
author
author
dc.subject.none.fl_str_mv Funcions enteres
Nuclis de Bergman
Funcions de diverses variables complexes
Anàlisi harmònica
Entire functions
Bergman kernel functions
Functions of several complex variables
Harmonic analysis
topic Funcions enteres
Nuclis de Bergman
Funcions de diverses variables complexes
Anàlisi harmònica
Entire functions
Bergman kernel functions
Functions of several complex variables
Harmonic analysis
description Answering a question of Lindholm, we prove strict density inequalities for sampling and interpolation in Fock spaces of entire functions in several complex variables defined by a plurisubharmonic weight. In particular, these spaces do not admit a set that is simultaneously sampling and interpolating. To prove optimality of the density conditions, we construct sampling sets with a density arbitrarily close to the critical density. The techniques combine methods from several complex variables (estimates for $\bar \partial$) and the theory of localized frames in general reproducing kernel Hilbert spaces (with no analyticity assumed). The abstract results on Fekete points and deformation of frames may be of independent interest.
publishDate 2019
dc.date.none.fl_str_mv 2019
2020
2020
2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/164420
url https://hdl.handle.net/2445/164420
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1016/j.jfa.2019.108282
Journal of Functional Analysis, 2019, vol. 277, num. 12
https://doi.org/10.1016/j.jfa.2019.108282
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Elsevier, 2019
http://creativecommons.org/licenses/by-nc-nd/3.0/es
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Elsevier, 2019
http://creativecommons.org/licenses/by-nc-nd/3.0/es
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 Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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