Wick calculus on spaces of generalized functions of compound poisson white noise

We derive white noise calculus for a compound Poisson process. Namely, we consider, on the Schwartz space of tempered distributions, S′, a measure of compound Poisson white noise, μcp, and construct a whole scale of standard nuclear triples (Scp)−x ⊃ L2cp) ≡ L2(S′, dμcp) ⊃(Scpx, x≥ 0, which are obtained as images under some isomorphism of the corresponding triples centred at a Fock space. It turns out that the most interesting case is x = 1, when our triple coincides with the triple that is constructed by using a system of Appell polynomials in the framework of non-Gaussian biorthogonal analysis. Our special attention is paid to the Wick calculus of the Poisson field, or the quantum compound Poisson white noise process in other terms, which is the family of operators acting from (Scp)1 into (Scp)1 as multiplication by the compound Poisson white noise ω(t).