An analytic characterization of \((p,q)\)-white noise functionals (Q2228164)

Summary: In this paper, a characterization theorem for the \(\mathcal{S}\)-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.