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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Authors: Gröchenig, Karlheinz, Haimi, Antti, Ortega Cerdà, Joaquim, Romero, José Luis
Format: article
Status:Versión aceptada para publicación
Publication Date:2019
Country:España
Institution:Universidad de Barcelona
Repository:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/164420
Online Access:https://hdl.handle.net/2445/164420
Access Level:Open access
Keyword: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.Elsevier2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/164420Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió 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:diposit.ub.edu:2445/1644202026-05-27T06:46:51Z
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
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
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:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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