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The measure transition problem for meromorphic polar functions

dc.contributor.authorBuescu, Jorge
dc.contributor.authorPaixão, António
dc.date.accessioned2021-06-21T14:11:11Z
dc.date.available2021-06-21T14:11:11Z
dc.date.issued2020-10-26
dc.description.abstractIn very general conditions, meromorphic polar functions (i.e. functions exhibiting some kind of positive or co-positive definiteness) separate the complex plane into horizontal or vertical strips of holomophy and polarity, in each of which they are characterized as integral transforms of exponentially finite measures. These measures characterize both the function and the strip. We study the problem of transition between different holomorphy strips, proving a transition formula which relates the measures on neighbouring strips of polarity. The general transition problem is further complicated by the fact that a function may lose polarity upon strip crossing and in general we cannot expect polarity, or even some specific related form of integral representation, to exist. We show that, even in these cases, a relevant analytical role will be played by exponentially finite signed measures, which we construct and study. Applications to especially significant examples like the Gamma, zeta or Bessel functions are performed.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationBUESCU, Jorge; PAIXÃO, António C. – The measure transition problem for meromorphic polar functions. Analysis and Mathematical Physics. ISSN 1664-2368. Vol. 10, N.º 4 (2020), pp. 1-41pt_PT
dc.identifier.doi10.1007/s13324-020-00408-wpt_PT
dc.identifier.eissn1664-235X
dc.identifier.issn1664-2368
dc.identifier.urihttp://hdl.handle.net/10400.21/13459
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSpringerpt_PT
dc.relationUID/MAT/04561/2019 - FCT European Commissionpt_PT
dc.subjectMeromorphic functionspt_PT
dc.subjectPositive definite functionspt_PT
dc.subjectMeasure theorypt_PT
dc.subjectFourier transformpt_PT
dc.subjectLaplace transformpt_PT
dc.subjectGamma functionpt_PT
dc.subjectZeta functionpt_PT
dc.titleThe measure transition problem for meromorphic polar functionspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage41pt_PT
oaire.citation.issue4pt_PT
oaire.citation.startPage1pt_PT
oaire.citation.titleAnalysis and Mathematical Physicspt_PT
oaire.citation.volume10pt_PT
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.latestForDiscovery794cf4b2-ce83-40ab-bc77-d53913d6a851

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