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An abstract form of a theorem of Helson and applications to sets of synthesis and sets of uniqueness

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dc.contributor.departmentDepartment of Mathematics
dc.contributor.facultymemberYes
dc.contributor.kuauthorÜlger, Ali
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T22:59:38Z
dc.date.issued2010
dc.description.abstractLet E be a compact perfect subset of the real line R such that the restriction of the Fourier transform a bar right arrow (a) over cap vertical bar(E) from L(1)(R) into C(E) is onto. Helson proved that then, for mu is an element of M(E), lim(vertical bar y vertical bar ->infinity vertical bar) (u) over cap (y)vertical bar = 0 is possible only if mu = 0. In this paper we present an abstract version of this theorem of Helson and provide some applications of it to the study of sets of spectral synthesis and sets of uniqueness.
dc.description.fulltextNo
dc.description.harvestedfromManual
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.openaccessYES
dc.description.peerreviewstatusN/A
dc.description.publisherscopeInternational
dc.description.readpublishN/A
dc.description.sponsoredbyTubitakEuTÜBİTAK
dc.description.sponsorshipThis work of the author is partially supported by Turkish Academy of Sciences and Tubitak Isbap-Project No.107T896.
dc.description.studentonlypublicationNo
dc.description.studentpublicationNo
dc.description.versionN/A
dc.identifier.WoSQuartileQ1
dc.identifier.doi10.1016/j.jfa.2009.09.021
dc.identifier.embargoN/A
dc.identifier.endpage977
dc.identifier.grantno107T896
dc.identifier.issn0022-1236
dc.identifier.issue3
dc.identifier.scopus2-s2.0-70350596213
dc.identifier.startpage956
dc.identifier.urihttps://doi.org/10.1016/j.jfa.2009.09.021
dc.identifier.urihttps://hdl.handle.net/20.500.14288/7927
dc.identifier.volume258
dc.identifier.wos000272112900011
dc.keywordsHelson set
dc.keywordsSet of synthesis
dc.keywordsSet of uniqueness
dc.keywordsGroup algebra
dc.keywordsMultipliers
dc.keywordsArens product
dc.keywordsWeakly almost periodic functions
dc.keywordsNarrow spectral analysis
dc.keywordslocally compact-groups
dc.keywordsPeriodic functions
dc.keywordsFourier algebra
dc.keywordsKronecker
dc.keywordsRn
dc.language.isoeng
dc.publisherAcademic Press Inc
dc.relation.affiliationKoç University
dc.relation.collectionKoç University Institutional Repository
dc.relation.ispartofJournal of Functional Analysis
dc.relation.openaccessN/A
dc.rightsN/A
dc.subjectMathematics
dc.titleAn abstract form of a theorem of Helson and applications to sets of synthesis and sets of uniqueness
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorÜlger, Ali
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relation.isOrgUnitOfPublication.latestForDiscovery2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
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