Asymptotics of the Fourier and Laplace transforms in weighted spaces of analytic functions

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dc.creatorMatsaev, Vladimir
dc.creatorSodin, Mikhail
dc.date2001-11-04
dc.date.accessioned2026-07-07T06:30:19Z
dc.date.available2026-07-07T06:30:19Z
dc.descriptionWe study the asymptotics near the origin of the Fourier transform in weighted Hardy spaces of analytic functions in the upper half-plane, and of the Laplace transform in weighted spaces of entire functions of zero exponential type. These results are applied to two closely related problems posed by E. Dyn'kin: we find the asymptotics of the depth of zero in non-quasianalytic Denjoy-Carleman classes, and of the exact Levinson-Sjoberg majorant.
dc.descriptionLATeX, 38 pages, preliminary version
dc.identifierhttps://arxiv.org/abs/math/0111037
dc.identifierhttp://arxiv.org/abs/math/0111037
dc.identifierAlgebra i Analiz 14 (2002), no. 4, 107--140; translation in St. Petersburg Math. J. 14 (2003), no. 4, 615--640
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98312
dc.subjectComplex Variables
dc.subjectClassical Analysis and ODEs
dc.titleAsymptotics of the Fourier and Laplace transforms in weighted spaces of analytic functions
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