Tensor Representation of Spaces of Holomorphic Functions and Applications

In this paper we study the tensor representation of spaces of Fr,chet-valued holomorphic functions in the form where U is an open subset of a Fr,chet space and Using this result we consider the following problems: exponential laws for the topologies on the space where U and V are two open subsets of locally convex spaces E and F respectively; the coincidence of the topologies on spaces of locally convex valued holomorphic functions (resp. germs) H(U, F) [resp. H(K, F)]; the inheritance of the properties (QNo), via the spaces of holomorphic functions and of holomorphic germs.