The space H(Ω, (zj)) of holomorphic functions

Let Omega be a domain in C-n. Let H(Omega) be the linear space over C of the holomorphic functions in Omega, endowed with the compact-open topology. Let (z(j)) be a sequence in Omega without adherent points in Omega. In this paper, we define the space H(Omega, (z(j))) and some of its linear topological properties are studied. We also show that, for some domains of holomorphy Omega and some sequences (z(j)), the non-zero elements of H(Omega, (z(j))) cannot be extended holomorphically outside Omega. As a consequence, we obtain some characterizations of the domains of holomorphy in C-n. (c) 2007 Elsevier Inc. All rights reserved.