Non-oscillating Paley-wiener functions

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dc.citation.epage232en_US
dc.citation.issueNumber1en_US
dc.citation.spage211en_US
dc.citation.volumeNumber92en_US
dc.contributor.authorOstrovskii, I. V.en_US
dc.contributor.authorUlanovskii, A.en_US
dc.date.accessioned2019-03-06T12:22:56Z
dc.date.available2019-03-06T12:22:56Z
dc.date.issued2004en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractA non-oscillating Paley-Wiener function is a real entire functionf of exponential type belonging toL 2(R) and such that each derivativef (n),n=0, 1, 2,…, has only a finite number of real zeros. It is established that the class of such functions is non-empty and contains functions of arbitrarily fast decay onR allowed by the convergence of the logarithmic integral. It is shown that the Fourier transform of a non-oscillating Paley-Wiener function must be infinitely differentiable outside the origin. We also give close to best possible asymptotic (asn→∞) estimates of the number of real zeros of then-th derivative of a functionf of the class and the size of the smallest interval containing these zeros.en_US
dc.identifier.doi10.1007/BF02787762en_US
dc.identifier.eissn1565-8538
dc.identifier.issn0021-7670
dc.identifier.urihttp://hdl.handle.net/11693/50651
dc.language.isoEnglishen_US
dc.publisherSpringer-Verlagen_US
dc.relation.isversionofhttps://doi.org/10.1007/BF02787762en_US
dc.source.titleJournal d’Analyse Mathématiqueen_US
dc.titleNon-oscillating Paley-wiener functionsen_US
dc.typeArticleen_US
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