Representable Functions on the Unit Ball of a Banach Space

Abstract

In this paper we treat the problem of integral representation of analytic functions over the unit ball of a complex Banach space X using the theory of abstract Wiener spaces. We define the class of representable functions on the unit ball of X and prove that this set of functions is related with the classes of integral k-homogeneous polynomials, integral holomorphic functions and also with the set of Lp-representable functions on a Banach space.