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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.kuauthorÜlger, Ali
dc.contributor.kuprofileFaculty Member
dc.contributor.otherDepartment of Mathematics
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.contributor.yokidN/A
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.indexedbyWoS
dc.description.indexedbyScopus
dc.description.issue3
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsorshipTurkish Academy of Sciences
dc.description.sponsorshipTUBITAKIsbap-Project [107T896] This work of the author is partially supported by Turkish Academy of Sciences and TUBITAKIsbap-Project No.107T896.
dc.description.volume258
dc.identifier.doi10.1016/j.jfa.2009.09.021
dc.identifier.issn0022-1236
dc.identifier.quartileQ1
dc.identifier.scopus2-s2.0-70350596213
dc.identifier.urihttp://dx.doi.org/10.1016/j.jfa.2009.09.021
dc.identifier.urihttps://hdl.handle.net/20.500.14288/7927
dc.identifier.wos272112900011
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.languageEnglish
dc.publisherAcademic Press Inc Elsevier Science
dc.sourceJournal of Functional Analysis
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.authorid0000-0002-3377-8666
local.contributor.kuauthorÜlger, Ali
relation.isOrgUnitOfPublication2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
relation.isOrgUnitOfPublication.latestForDiscovery2159b841-6c2d-4f54-b1d4-b6ba86edfdbe

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