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 L-2-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.