arXiv math/01110372001-11-04math.CVmath.CA

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

Vladimir Matsaev, Mikhail Sodin

备注：: LATeX, 38 pages, preliminary version
发表信息：: Algebra i Analiz 14 (2002), no. 4, 107--140; translation in St. Petersburg Math. J. 14 (2003), no. 4, 615--640

英文摘要：

We 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.

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