Construction of the log-convex minorant of a sequence {M_alpha}_alpha

[EN] We give a simple construction of the log-convex minorant of a sequence {M_alpha}_alpha and consequently extend to the d-dimensional case the well-known formula that relates a log-convex sequence {M_p} to its associated function omega(M), that is M_p=sup(t>0)t(p)exp(-omega(M)(t)). We show...

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Authors: Boiti, Chiara, Oliaro, Alessandro, Schindl, Gerhard, Jornet Casanova, David|||0000-0002-3531-6203
Format: article
Publication Date:2024
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/213363
Online Access:https://riunet.upv.es/handle/10251/213363
Access Level:Open access
Keyword:Log-convex sequences
Matrix weights
Regularization of sequences
Ultradifferentiable functions
MATEMATICA APLICADA
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spelling Construction of the log-convex minorant of a sequence {M_alpha}_alphaBoiti, ChiaraOliaro, AlessandroSchindl, GerhardJornet Casanova, David|||0000-0002-3531-6203Log-convex sequencesMatrix weightsRegularization of sequencesUltradifferentiable functionsMATEMATICA APLICADA[EN] We give a simple construction of the log-convex minorant of a sequence {M_alpha}_alpha and consequently extend to the d-dimensional case the well-known formula that relates a log-convex sequence {M_p} to its associated function omega(M), that is M_p=sup(t>0)t(p)exp(-omega(M)(t)). We show that in the more dimensional anisotropic case the classical log-convex condition M-alpha(2)<= M alpha-ejM alpha+ej is not sufficient: convexity as a function of more variables is needed (not only coordinate-wise). We finally obtain some applications to the inclusion of spaces of rapidly decreasing ultradifferentiable functions in the matrix weighted setting.The authors are sincerely grateful to Prof. Andreas Debrouwere for pointing out that the argument in the first version of the proof of Theorem 4.1 was incomplete, and they thank the referees for their helpful suggestions to improve the paper. Boiti and Oliaro were partially supported by the INdAM-GNAMPA Project 2023 "Analisi di Fourier e Analisi Tempo-Frequenza di Spazi Funzionali ed Operatori", CUP_ E53C22001930001. Boiti was partially supported by the Projects FAR 2020, FAR 2021, FAR 2022, FIRD 2022, and FAR 2023 (University of Ferrara). Jornet is partially supported by the project PID2020-119457GB-100 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe." The research of the fourth author was funded in whole by the Austrian Science Fund (FWF) project 10.55776/P33417.John Wiley & SonsDepartamento de Matemática AplicadaEscuela Técnica Superior de ArquitecturaInstituto Universitario de Matemática Pura y AplicadaAustrian Science FundAgencia Estatal de InvestigaciónEuropean Regional Development FundUniversità degli Studi di FerraraMinistero dell'Istruzione, dell'Università e della RicercaRepositorio Institucional de la Universitat Politècnica de València Riunet20242024-11-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/213363reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-119457GB-I00 METODOS DEL ANALISIS FUNCIONAL PARA LA TEORIA DE OPERADORES Y EL ANALISIS TIEMPO-FRECUENCIAMinistero dell'Istruzione dell'Università e della Ricerca, Italia https://doi.org/10.13039/501100003407 CUP E53C22001930001Austrian Science Fund https://doi.org/10.13039/501100002428 P33417Union des Industries Ferroviaires Européennes https://doi.org/10.13039/501100007109 FAR2021Union des Industries Ferroviaires Européennes https://doi.org/10.13039/501100007109 FAR2023Union des Industries Ferroviaires Européennes https://doi.org/10.13039/501100007109 FAR2020Union des Industries Ferroviaires Européennes https://doi.org/10.13039/501100007109 FAR2022Union des Industries Ferroviaires Européennes https://doi.org/10.13039/501100007109 FIRD2022open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2133632026-06-13T07:49:27Z
dc.title.none.fl_str_mv Construction of the log-convex minorant of a sequence {M_alpha}_alpha
title Construction of the log-convex minorant of a sequence {M_alpha}_alpha
spellingShingle Construction of the log-convex minorant of a sequence {M_alpha}_alpha
Boiti, Chiara
Log-convex sequences
Matrix weights
Regularization of sequences
Ultradifferentiable functions
MATEMATICA APLICADA
title_short Construction of the log-convex minorant of a sequence {M_alpha}_alpha
title_full Construction of the log-convex minorant of a sequence {M_alpha}_alpha
title_fullStr Construction of the log-convex minorant of a sequence {M_alpha}_alpha
title_full_unstemmed Construction of the log-convex minorant of a sequence {M_alpha}_alpha
title_sort Construction of the log-convex minorant of a sequence {M_alpha}_alpha
dc.creator.none.fl_str_mv Boiti, Chiara
Oliaro, Alessandro
Schindl, Gerhard
Jornet Casanova, David|||0000-0002-3531-6203
author Boiti, Chiara
author_facet Boiti, Chiara
Oliaro, Alessandro
Schindl, Gerhard
Jornet Casanova, David|||0000-0002-3531-6203
author_role author
author2 Oliaro, Alessandro
Schindl, Gerhard
Jornet Casanova, David|||0000-0002-3531-6203
author2_role author
author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Arquitectura
Instituto Universitario de Matemática Pura y Aplicada
Austrian Science Fund
Agencia Estatal de Investigación
European Regional Development Fund
Università degli Studi di Ferrara
Ministero dell'Istruzione, dell'Università e della Ricerca
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Log-convex sequences
Matrix weights
Regularization of sequences
Ultradifferentiable functions
MATEMATICA APLICADA
topic Log-convex sequences
Matrix weights
Regularization of sequences
Ultradifferentiable functions
MATEMATICA APLICADA
description [EN] We give a simple construction of the log-convex minorant of a sequence {M_alpha}_alpha and consequently extend to the d-dimensional case the well-known formula that relates a log-convex sequence {M_p} to its associated function omega(M), that is M_p=sup(t>0)t(p)exp(-omega(M)(t)). We show that in the more dimensional anisotropic case the classical log-convex condition M-alpha(2)<= M alpha-ejM alpha+ej is not sufficient: convexity as a function of more variables is needed (not only coordinate-wise). We finally obtain some applications to the inclusion of spaces of rapidly decreasing ultradifferentiable functions in the matrix weighted setting.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-11-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/213363
url https://riunet.upv.es/handle/10251/213363
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 PID2020-119457GB-I00 METODOS DEL ANALISIS FUNCIONAL PARA LA TEORIA DE OPERADORES Y EL ANALISIS TIEMPO-FRECUENCIA
Ministero dell'Istruzione dell'Università e della Ricerca, Italia https://doi.org/10.13039/501100003407 CUP E53C22001930001
Austrian Science Fund https://doi.org/10.13039/501100002428 P33417
Union des Industries Ferroviaires Européennes https://doi.org/10.13039/501100007109 FAR2021
Union des Industries Ferroviaires Européennes https://doi.org/10.13039/501100007109 FAR2023
Union des Industries Ferroviaires Européennes https://doi.org/10.13039/501100007109 FAR2020
Union des Industries Ferroviaires Européennes https://doi.org/10.13039/501100007109 FAR2022
Union des Industries Ferroviaires Européennes https://doi.org/10.13039/501100007109 FIRD2022
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/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
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv John Wiley & Sons
publisher.none.fl_str_mv John Wiley & Sons
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
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repository.mail.fl_str_mv
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