On the space of Laplace transformable distributions

Abstract

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