A note on holomorphic functions and the Fourier-Laplace transform

• Marcus Carlsson ^[1] ; Jens Wittsten
  1. [1] Lund University-SWEDEN
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 120, Nº 2, 2017, págs. 225-248
• Idioma: inglés
• DOI: 10.7146/math.scand.a-25612
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• Resumen

  • 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 (−∞,b], b∈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 Hp(C+).