(DFS)-spaces of holomorphic functions invariant under differentiation

Let G ⊂ C be a bounded convex domain, A−∞(G) be the (DFS)-space of all holomorphic functions of polynomial growth on G and A∞(G) be the Fréchet space of C∞-functions on closure G of G which are holomorphic on G. With the help of the Laplace transform we describe the strong dual of A−∞(G) and prove that A−∞(G) is the unique (DFS)-space H such that the space A∞(G) is contained in H, H is embedded continuously in A−∞(G) and H is invariant under differentiation.  2004 Elsevier Inc. All rights reserved