Paley–Wiener–Schwartz Type Theorem for Ultradistributions on an Unbounded Closed Convex Set

Abstract

We consider the subspace of the Schwartz space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in a multidimensional real space equipped with the topology defined by a countable family of norms constructed with the help of a family of convex separately radial functions in ℝn. We describe the strong dual of this subspace in terms of the Fourier–Laplace transform of functionals.