Fock space associated with quadrabasic Hermite orthogonal polynomials

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.

The Double Fock Space of Type B

“…In the present version of the model, we apply a more natural operation on tensor product, which finally contributes to the more natural combinatorics of calculating the Gaussian moments. In [10], we put the action of the symmetrization on n points but in the current approach we give 2n points which is close to our construction from the articles [9,20]. In [10], we defined the creator in the same way as in the case of type A, and then we did not obtain a natural combinatorics which is compatible with partitions of the set {±1, .…”