Extension operators for some ultraholomorphic classes defined by sequences of rapid growth

While the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid growth, there is no general procedure to construct extension op...

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Detalhes bibliográficos
Autores: Jiménez Garrido, Javier, Lastra Sedano, Alberto|||0000-0002-4012-6471, Sanz, Javier
Formato: artículo
Fecha de publicación:2023
País:España
Recursos:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/60200
Acesso em linha:http://hdl.handle.net/10017/60200
https://dx.doi.org/10.1007/s00365-023-09663-z
Access Level:acceso abierto
Palavra-chave:Linear extension operators
Asymptotic expansions
Carleman ultraholomorphic classes
Lambert function
Laplace transform
Matemáticas
Mathematics
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spelling Extension operators for some ultraholomorphic classes defined by sequences of rapid growthJiménez Garrido, JavierLastra Sedano, Alberto|||0000-0002-4012-6471Sanz, JavierLinear extension operatorsAsymptotic expansionsCarleman ultraholomorphic classesLambert functionLaplace transformMatemáticasMathematicsWhile the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid growth, there is no general procedure to construct extension operators in this case. We do provide such operators in complex sectors for some particular classes considered by S. Pilipović, N. Teofanov and F. Tomić in the ultradifferentiable setting. Although these classes are, in their words, “beyond Gevrey regularity”, in some cases they keep the property of stability under differentiation, which is crucial for our technique, based on formal Borel- and truncated Laplace-like transforms with suitable kernels.Agencia Estatal de InvestigaciónUniversidad de AlcaláSpringer20232023-07-1520232023-07-1520242024-07-15journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10017/60200https://dx.doi.org/10.1007/s00365-023-09663-zreponame:e_Buah Biblioteca Digital Universidad de Alcaláinstname:Universidad de Alcalá (UAH)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-105621GB-I00 METODOS ASINTOTICOS, ALGEBRAICOS Y GEOMETRICOS EN FOLIACIONES SINGULARES Y SISTEMAS DINAMICOSUAH Not available CM-JIN-2021-014Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica, Técnica y de Innovación 2021-2023 TED2021-129813A-I00open accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ebuah.uah.es:10017/602002026-06-18T11:13:07Z
dc.title.none.fl_str_mv Extension operators for some ultraholomorphic classes defined by sequences of rapid growth
title Extension operators for some ultraholomorphic classes defined by sequences of rapid growth
spellingShingle Extension operators for some ultraholomorphic classes defined by sequences of rapid growth
Jiménez Garrido, Javier
Linear extension operators
Asymptotic expansions
Carleman ultraholomorphic classes
Lambert function
Laplace transform
Matemáticas
Mathematics
title_short Extension operators for some ultraholomorphic classes defined by sequences of rapid growth
title_full Extension operators for some ultraholomorphic classes defined by sequences of rapid growth
title_fullStr Extension operators for some ultraholomorphic classes defined by sequences of rapid growth
title_full_unstemmed Extension operators for some ultraholomorphic classes defined by sequences of rapid growth
title_sort Extension operators for some ultraholomorphic classes defined by sequences of rapid growth
dc.creator.none.fl_str_mv Jiménez Garrido, Javier
Lastra Sedano, Alberto|||0000-0002-4012-6471
Sanz, Javier
author Jiménez Garrido, Javier
author_facet Jiménez Garrido, Javier
Lastra Sedano, Alberto|||0000-0002-4012-6471
Sanz, Javier
author_role author
author2 Lastra Sedano, Alberto|||0000-0002-4012-6471
Sanz, Javier
author2_role author
author
dc.subject.none.fl_str_mv Linear extension operators
Asymptotic expansions
Carleman ultraholomorphic classes
Lambert function
Laplace transform
Matemáticas
Mathematics
topic Linear extension operators
Asymptotic expansions
Carleman ultraholomorphic classes
Lambert function
Laplace transform
Matemáticas
Mathematics
description While the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid growth, there is no general procedure to construct extension operators in this case. We do provide such operators in complex sectors for some particular classes considered by S. Pilipović, N. Teofanov and F. Tomić in the ultradifferentiable setting. Although these classes are, in their words, “beyond Gevrey regularity”, in some cases they keep the property of stability under differentiation, which is crucial for our technique, based on formal Borel- and truncated Laplace-like transforms with suitable kernels.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-07-15
2023
2023-07-15
2024
2024-07-15
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10017/60200
https://dx.doi.org/10.1007/s00365-023-09663-z
url http://hdl.handle.net/10017/60200
https://dx.doi.org/10.1007/s00365-023-09663-z
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2019-105621GB-I00 METODOS ASINTOTICOS, ALGEBRAICOS Y GEOMETRICOS EN FOLIACIONES SINGULARES Y SISTEMAS DINAMICOS
UAH Not available CM-JIN-2021-014
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica, Técnica y de Innovación 2021-2023 TED2021-129813A-I00
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:e_Buah Biblioteca Digital Universidad de Alcalá
instname:Universidad de Alcalá (UAH)
instname_str Universidad de Alcalá (UAH)
reponame_str e_Buah Biblioteca Digital Universidad de Alcalá
collection e_Buah Biblioteca Digital Universidad de Alcalá
repository.name.fl_str_mv
repository.mail.fl_str_mv
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