Pascal white noise harmonic analysis on configuration spaces and applications

Author:

Riahi Anis1,Rebei Habib1

Affiliation:

1. Department of Mathematics, College of Science, Qassim University, Kingdom of Saudi Arabia

Abstract

In this paper, we unify techniques of Pascal white noise analysis and harmonic analysis on configuration spaces establishing relations between the main structures of both ones. Fix a Random measure [Formula: see text] on a Riemannian manifold [Formula: see text], we construct on the space of finite compound configuration space [Formula: see text] the so-called Lebesgue–Pascal measure [Formula: see text] and as a consequence we obtain the Pascal measure [Formula: see text] on the compound configuration space [Formula: see text]. Next, the natural realization of the symmetric Fock space over [Formula: see text] as the space [Formula: see text] leads to the unitary isomorphism [Formula: see text] between the space [Formula: see text] and [Formula: see text]. Finally, in the first application we study some algebraic products, namely, the Borchers product on the Fock space, the Wick product on the Pascal space, and the ⋆-convolution on the Lebesgue–Pascal space and we prove that the Pascal white noise analysis and harmonic analysis are related through an equality of operators involving [Formula: see text]. The second application is devoted to solve the implementation problem.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Fractional Gamma Noise Functionals;Complex Analysis and Operator Theory;2024-05

2. Polynomial sequences associated with the fractional Pascal measure;Integral Transforms and Special Functions;2024-03-18

3. A chaotic decomposition for the fractional Lebesgue–Pascal noise space;Random Operators and Stochastic Equations;2023-02-28

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