This article is cited in 5 papers

A Theorem of Paley–Wiener Type for Ultradistributions

I. Kh. Musin, P. V. Fedotova

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: Using the Fourier–Laplace transformation of functionals, we give a description of the spaces dual to the spaces of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in $\mathbb R^n$.

Keywords: ultradistribution, Paley–Wiener theorem, Fourier–Laplace transformation, holomorphic function, plurisubharmonic function, Lebesgue measure.

UDC: 517.982.3

Received: 22.11.2007
Revised: 07.11.2008

DOI: 10.4213/mzm4414

 English version: Mathematical Notes, 2009, 85:6, 848–867

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