Lp-representable functions on Banach spaces

In this paper we discuss the problem of integral representation of analytic functions over a complex Banach space E. We define the class of Lp-representable and ρ-representable functions and prove that they verify some growth conditions. The aim of this work is to characterize these classes of functions. It is also shown that it is possible to give an alternative representation for integral polynomials over a Hilbert space H using a universal Wiener measure. © 2007 Elsevier Inc. All rights reserved.