Integral representation of holomorphic functions on Banach spaces

In this paper we discuss the problem of integral representation of analytic functions over a complex Banach space E. We obtain, for a wide class of functions, integral representations of the form f (x) = E eγ (x)f1(γ ) dW(γ ) and f (x) = E 1 1− γ (x) γ f2(γ ) dW(γ ), where W is an abstract Wiener measure on E and f1,f2 are transformations of f involving the covariance operator of W.  2004 Elsevier Inc. All rights reserved