On the space of Laplace transformable distributions

Abstract

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

10 pages