Positive-definiteness and integral representations for special functions

Detalhes bibliográficos
Autor(a) principal: Buescu, Jorge
Data de Publicação: 2020
Outros Autores: Paixão, António
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.21/12608
Resumo: It is known that a holomorphic positive definite function f defined on a horizontal strip of the complex plane may be characterized as the Fourier-Laplace transform of a unique exponentially finite measure on R. In this paper we apply this complex integral representation to specific families of special functions, including the Gamma, zeta and Bessel functions, and construct explicitly the corresponding measures, thus providing new insight into the nature of complex positive and co-positive definite functions. In the case of the zeta function this process leads to a new proof of an integral representation on the critical strip.
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spelling Positive-definiteness and integral representations for special functionsPositive definite functionsFourier-Laplace transformCharacteristic functionsHolomorphyGamma functionZeta functionExponentially convex functionsIt is known that a holomorphic positive definite function f defined on a horizontal strip of the complex plane may be characterized as the Fourier-Laplace transform of a unique exponentially finite measure on R. In this paper we apply this complex integral representation to specific families of special functions, including the Gamma, zeta and Bessel functions, and construct explicitly the corresponding measures, thus providing new insight into the nature of complex positive and co-positive definite functions. In the case of the zeta function this process leads to a new proof of an integral representation on the critical strip.SpringerRCIPLBuescu, JorgePaixão, António2021-01-14T12:45:42Z2020-082020-08-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/12608engBUESCU, J.; PAIXÃO, António Carlos – Positive-definiteness and integral representations for special functions. Positivity. ISSN 1385-1292. Vol. 25, N.º 2 (2020), pp. 731-7501385-129210.1007/s11117-020-00784-4metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T10:05:51Zoai:repositorio.ipl.pt:10400.21/12608Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:20:39.862506Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Positive-definiteness and integral representations for special functions
title Positive-definiteness and integral representations for special functions
spellingShingle Positive-definiteness and integral representations for special functions
Buescu, Jorge
Positive definite functions
Fourier-Laplace transform
Characteristic functions
Holomorphy
Gamma function
Zeta function
Exponentially convex functions
title_short Positive-definiteness and integral representations for special functions
title_full Positive-definiteness and integral representations for special functions
title_fullStr Positive-definiteness and integral representations for special functions
title_full_unstemmed Positive-definiteness and integral representations for special functions
title_sort Positive-definiteness and integral representations for special functions
author Buescu, Jorge
author_facet Buescu, Jorge
Paixão, António
author_role author
author2 Paixão, António
author2_role author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Buescu, Jorge
Paixão, António
dc.subject.por.fl_str_mv Positive definite functions
Fourier-Laplace transform
Characteristic functions
Holomorphy
Gamma function
Zeta function
Exponentially convex functions
topic Positive definite functions
Fourier-Laplace transform
Characteristic functions
Holomorphy
Gamma function
Zeta function
Exponentially convex functions
description It is known that a holomorphic positive definite function f defined on a horizontal strip of the complex plane may be characterized as the Fourier-Laplace transform of a unique exponentially finite measure on R. In this paper we apply this complex integral representation to specific families of special functions, including the Gamma, zeta and Bessel functions, and construct explicitly the corresponding measures, thus providing new insight into the nature of complex positive and co-positive definite functions. In the case of the zeta function this process leads to a new proof of an integral representation on the critical strip.
publishDate 2020
dc.date.none.fl_str_mv 2020-08
2020-08-01T00:00:00Z
2021-01-14T12:45:42Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.21/12608
url http://hdl.handle.net/10400.21/12608
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv BUESCU, J.; PAIXÃO, António Carlos – Positive-definiteness and integral representations for special functions. Positivity. ISSN 1385-1292. Vol. 25, N.º 2 (2020), pp. 731-750
1385-1292
10.1007/s11117-020-00784-4
dc.rights.driver.fl_str_mv metadata only access
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eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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