An Analytic Characterization of p, q-White Noise Functionals. (8th December 2020)

• Record Type: Journal Article
• Authors: Riahi, Anis; Ettaieb, Amine; Chammam, Wathek; Alhussain, Ziyad Ali
• Other Names: Fu Yongqiang Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2020(2020)
• Publication Date: 2020-12-08
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2020/6319138
• Languages: English
• ISSNs: 2314-4629

Abstract

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.