Fock space associated with quadrabasic Hermite orthogonal polynomials

2020/04/18 by Wiktor Ejsmont, Ejsmont, Wiktor
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Operator Algebras (math.OA) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2004.08538

openalex publication_date 2020/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces a new idea for constructing operators associated with a certain class of probability measures. Special cases include several know classical and noncommutative probability. The main example is derived from Feller [30, Page 503, Example 10], i.e. the hyperbolic secant distribution. In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function.

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