Homomorphisms on spaces of weakly continuous holomorphic functions

Let X be a Banach space and let X* be its topological dual space. We study the algebra H-w*(X*) of entire functions on X* that are weak-star continuou s on bounded sets. We prove that every m-homogeneous polynomial of finite t ype P on X* that is weak-star continuous on bounded sets can be written in the form P = [GRAPHICS] where x(ij) epsilon X, for all i,j. As an application, we characterize canv olution homomorphisms on H-w* (X*) and on the space H-wu(X) of entire funct ions on X which are weakly uniformly continuous on bounded subsets of X, as suming that X* has the approximation property.