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)andf(x)=∫E′11−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.