Let 𝒩* be a Hilbert inductive limit and X a Banach space. In this paper, we obtain a necessary and sufficient condition for an analytic mapping Ψ:𝒩*↦X to have a factorization of the form Ψ=T∘ℰ, where ℰ is the exponential mapping on 𝒩* and T:Γ(𝒩*)↦X is a continuous linear operator, where Γ(𝒩*) denotes the Boson Fock space over 𝒩*. To prove this result, we establish some kernel theorems for multilinear mappings defined on multifold Cartesian products of a Hilbert space and valued in a Banach space, which are of interest in their own right. We also apply the above factorization result to white noise theory and get a characterization theorem for white noise testing functionals.
Email your librarian or administrator to recommend adding this journal to your organisation's collection.
* Views captured on Cambridge Core between September 2016 - 28th June 2017. This data will be updated every 24 hours.