Integral representation of holomorphic mappings on fully nuclear spaces

We obtain the following integral representation: f (z) = E β e z,w · (f ◦D)(w) dμγ (w) for all z ∈ E, a fully nuclear space with basis, where η and γ belong to E β , η/γ ∈ 1, f is a holomorphic function of η-exponential type on E, μγ is a Gaussian measure on E β , and D is a densely defined diagonal mapping from E β into E. © 2007 Elsevier Inc. All rights reserved