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

Vladimir Matsaev·Mikhail Sodin
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Abstract

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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Vladimir Matsaev, Mikhail Sodin. 2001-11-04. Asymptotics of the Fourier and Laplace transforms in weighted spaces of analytic functions. https://arxiv.org/abs/math/0111037

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