On the space of Laplace transformable distributions.

Abstract

We show that the space $S^{\text{'}}\left(\Gamma \right)$ of Laplace transformable distributions, where $\Gamma \subseteq R^d$ is a non-empty convex open set, is an ultrabornological (PLS)-space. Moreover, we determine an explicit topological predual of $S^{\text{'}}\left(\Gamma \right)$ .