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

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

2001-11-04

arxiv.org/abs/math/0111037v1

Algebra i Analiz 14 (2002), no. 4, 107--140; translation in St. Petersburg Math. J. 14 (2003), no. 4, 615--640

Mathematics

Complex Variables

LATeX, 38 pages, preliminary version

Scientific paper

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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