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

Vladimir Matsaev; Mikhail Sodin

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

Complex Variables 2007-05-23 v1 Classical Analysis and ODEs

Authors: Vladimir Matsaev , Mikhail Sodin

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.

Keywords

fourier transform laplace transform weighted hardy spaces entire functions asymptotics denjoy-carleman classes

Cite

@article{arxiv.math/0111037,
  title  = {Asymptotics of the Fourier and Laplace transforms in weighted spaces of analytic functions},
  author = {Vladimir Matsaev and Mikhail Sodin},
  journal= {arXiv preprint arXiv:math/0111037},
  year   = {2007}
}

Comments

LATeX, 38 pages, preliminary version

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

Abstract

Keywords

Cite

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