An Analytic Characterization of p,q-White Noise Functionals

Abstract

In this paper, a characterization theorem for the S-transform of infinite dimensional distributions of noncommutative white noise corresponding to the p,q-deformed quantum oscillator algebra is investigated. We derive a unitary operator U between the noncommutative L2-space and the p,q-Fock space which serves to give the construction of a white noise Gel’fand triple. Next, a general characterization theorem is proven for the space of p,q-Gaussian white noise distributions in terms of new spaces of p,q-entire functions with certain growth rates determined by Young functions and a suitable p,q-exponential map.