Real version of Paley-Wiener-Schwartz theorem for ultradistributions with ultradifferentiable singular support
Bull. Korean Math. Soc. 1999 Vol. 36, No. 3, 483-493
Jonggyu Cho and Kwang Whoi Kim
Seoul National University, Jeonju University
Abstract : We extend the Paley-Wiener-Schwartz theorem to the space of ultradistributions with respect to ultradifferentiable singular support and obtain its real version. That is, we obtain the growth condition in some tubular neighborhood of $\Bbb R^n$ of the Fourier transform of ultradistributions of Roumieu (or Beurling) type with ultradifferentiable singular support contained in a ball centered at the origin, and its real version.
Keywords : Paley-Wiener-Schwartz theorem, ultradistribution, ultradifferentiable singular support
MSC numbers : Primary 46F05; Secondary 42B10
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