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Positive-definiteness and integral representations for special functions

2020-08Journal article Open access
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dc.contributor.authorBuescu, Jorge
dc.contributor.authorPaixão, António
dc.date.accessioned2021-01-14T12:45:42Z
dc.date.available2021-01-14T12:45:42Z
dc.date.issued2020-08
dc.description.abstractIt 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.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationBUESCU, J.; PAIXÃO, António Carlos – Positive-definiteness and integral representations for special functions. Positivity. ISSN 1385-1292. Vol. 25, N.º 2 (2020), pp. 731-750pt_PT
dc.identifier.doi10.1007/s11117-020-00784-4pt_PT
dc.identifier.issn1385-1292
dc.identifier.issn1572-9281
dc.identifier.urihttp://hdl.handle.net/10400.21/12608
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSpringerpt_PT
dc.relationUID/MAT/04561/2019 - FCTpt_PT
dc.relation.publisherversionhttps://link.springer.com/article/10.1007/s11117-020-00784-4pt_PT
dc.subjectPositive definite functionspt_PT
dc.subjectFourier-Laplace transformpt_PT
dc.subjectCharacteristic functionspt_PT
dc.subjectHolomorphypt_PT
dc.subjectGamma functionpt_PT
dc.subjectZeta functionpt_PT
dc.subjectExponentially convex functionspt_PT
dc.titlePositive-definiteness and integral representations for special functionspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage750pt_PT
oaire.citation.issue2
oaire.citation.startPage731pt_PT
oaire.citation.titlePositivitypt_PT
oaire.citation.volume25
person.familyNameBuescu
person.familyNamePaixão
person.givenNameJorge
person.givenNameAntónio
person.identifier.ciencia-id631B-B789-52D5
person.identifier.orcid0000-0001-5444-5089
person.identifier.orcid0000-0003-3158-4195
person.identifier.scopus-author-id6507693814
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublicationad68e200-7e35-40ac-bfb2-071a53e19514
relation.isAuthorOfPublication794cf4b2-ce83-40ab-bc77-d53913d6a851
relation.isAuthorOfPublication.latestForDiscoveryad68e200-7e35-40ac-bfb2-071a53e19514

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