Integral representation of holomorphic mappings on fully nuclear spaces

We obtain the following integral representation:f(z)=∫Eβ′e〈z,w〉⋅(f○D)(w)dμγ(w) for all z∈Ez∈E, a fully nuclear space with basis, where η and γ   belong to Eβ′, η/γ∈ℓ1η/γ∈ℓ1, f is a holomorphic function of η-exponential type on E  , μγμγ is a Gaussian measure on Eβ′, and D   is a densely defined diagonal mapping from Eβ′ into E.