This article is cited in 1 paper

On a class of infinitely differentiable functions on unbounded convex set in $\mathbb R^n$ admitting holomorphic continuation in $\mathbb C^n$

I. Kh. Musin, P. V. Fedotova

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

Abstract: A subspace of the Schwartz space of rapidly decreasing functions on closed convex unbounded set in $\mathbb R^n$, admitting holomorphic extension in $\mathbb C^n$, is studied. The problem of description of the dual space for this space in terms of the Fourier-Laplace transform is considered.

Keywords: tube domain, tempered distributions, the Laplace transform of functionals, $\overline\partial$-problem.

UDC: 517.982.3

Received: 25.05.2009

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