The q-Meixner self-adjoint operators on the q-deformed Fock space (独立性と従属性の数理 : 函数解析学の視点から : RIMS研究集会報告集)

Hiroaki Yoshida

Hong-Yi Fan

Mohammed Daoud A, Y. Hassouni

Kamel Mezlini

Hiroaki Yoshida

In this paper, we consider the self-adjoint operator of the linear sum of the double q -creation, the double q -annihilation, the q -number, and the scalar operators on a q -deformed symmetric Fock space and investigate its distribution. By the self-adjointness of the operator, the theory of orthogonal polynomials can help us to determine the distributions well. It will be found that the distributions are in the types of the q -Meixner family.

Anis Riahi, Amine Ettaieb

In this paper we start with a new detailed construction of the one-mode type q-Lévy-Meixner Fock space [Formula: see text] which serves to obtain the quantum decomposition associated with the q-deformed Lévy-Meixner white noise processes. More precisely, based on the notion of quantum decomposition and the orthogonalization of polynomials of noncommutative q-Lévy-Meixner white noise [Formula: see text], we study the chaos property of the noncommutative L2-space with respect to the vacuum expectation τ. Next, we determine the distribution of the q-Lévy-Meixner operator J(χD) = ⟨ω, χD⟩ and as a consequence we give some useful properties of the q-Lévy-Meixner white noise process.