An Analytic Characterization of p,q-White Noise Functionals

Anis Riahi, Amine Ettaieb, Wathek Chammam, Ziyad Ali Alhussain and Yongqiang Fu

Journal of Mathematics, 2020, vol. 2020, 1-8

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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6319138

DOI: 10.1155/2020/6319138

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