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Complex positive definite functions on strips

2017-03Journal article Restricted access
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dc.contributor.authorBuescu, Jorge
dc.contributor.authorCoelho, Jose
dc.contributor.authorSymeonides, A.
dc.date.accessioned2017-11-07T11:26:43Z
dc.date.available2017-11-07T11:26:43Z
dc.date.issued2017-03
dc.description.abstractWe characterize a holomorphic positive definite function f defined on a horizontal strip of the complex plane as the Fourier–Laplace transform of a unique exponentially finite measure on R. With this characterization, the classical theorems of Bochner on positive definite functions and of Widder on exponentially convex functions become respectively the real and imaginary sections of the corresponding complex integral representation. We provide minimal holomorphy assumptions for this characterization and derive conclusions for meromorphic functions under minimal positive definiteness conditions. Further characterizations are derived from conditions on the derivatives of f arising from the study of the usual concepts of moment, moment-generating function and characteristic function in this context.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationBUESCU, Jorge; COELHO, José Augusto Paixão; SYMEONIDES, A. - Complex Positive Definite Functions on Strips. Complex Analysis and Operator Theory. ISSN 1661-8254. Vol. 11, N.º 3 (2017), pp 627-649pt_PT
dc.identifier.doi10.1007/s11785-015-0527-ypt_PT
dc.identifier.issn1661-8254
dc.identifier.issn1661-8262
dc.identifier.urihttp://hdl.handle.net/10400.21/7462
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSpringer Publishing Companypt_PT
dc.relation.publisherversionhttps://link.springer.com/content/pdf/10.1007%2Fs11785-015-0527-y.pdfpt_PT
dc.subjectPositive definite functionspt_PT
dc.subjectFourier–Laplace transformpt_PT
dc.subjectComplex analysispt_PT
dc.subjectCharacteristic functionspt_PT
dc.subjectMoment-generating functionspt_PT
dc.subjectExponentially convex functionspt_PT
dc.subjectMeromorphic functionspt_PT
dc.subjectZeta functionpt_PT
dc.titleComplex positive definite functions on stripspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F04561%2F2013/PT
oaire.citation.endPage649pt_PT
oaire.citation.issue3pt_PT
oaire.citation.startPage627pt_PT
oaire.citation.titleComplex Analysis and Operator Theorypt_PT
oaire.citation.volume11pt_PT
oaire.fundingStream5876
person.familyNameBuescu
person.familyNameCoelho
person.givenNameJorge
person.givenNameJose
person.identifierR-000-84M
person.identifier.ciencia-id631B-B789-52D5
person.identifier.ciencia-idD716-31DF-8371
person.identifier.orcid0000-0001-5444-5089
person.identifier.orcid0000-0001-8118-0864
person.identifier.ridG-2626-2011
person.identifier.scopus-author-id6507693814
person.identifier.scopus-author-id7101841005
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
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