A NOTE ON HOLOMORPHIC FUNCTIONS AND THE FOURIER-LAPLACE TRANSFORM

作者:Carlsson Marcus*; Wittsten Jens
来源:Mathematica Scandinavica, 2017, 120(2): 225-248.
DOI:10.7146/math.scand.a-25612

摘要

We revisit the classical problem of when a given function, which is analytic in the upper half plane C+, can be written as the Fourier transform of a function or distribution with support on a half axis (-infinity, b], b is an element of R. We derive slight improvements of the classical Paley-Wiener-Schwartz Theorem, as well as softer conditions for verifying membership in classical function spaces such as H-P (C+).

  • 出版日期2017