Fock space associated with quadrabasic Hermite orthogonal polynomials
Volume 270 / 2023
Studia Mathematica 270 (2023), 17-56
MSC: Primary 46L53; Secondary 47N30, 46L54.
DOI: 10.4064/sm210916-19-8
Published online: 28 February 2023
Abstract
This paper introduces a new idea for constructing operators associated with a certain class of probability measures. Special cases include known classical ones and noncommutative probability. The main example, derived from Feller’s book, is 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.
