Abstract
In this paper we start with a new detailed construction of the one-mode type q -Levy-Meixner Fock space F-LM((q))(H) which serves to obtain the quantum decomposition associated with the q-deformed Levy-Meixner white noise processes. More precisely, based on the notion of quantum decomposition and the orthogonalization of polynomials of noncommutative q-L ' evy-Meixner white noise omega (t) := b(t)* + c(2)b(t) + beta b(t)*b(t)(2)*+ gamma b(t)(*)b(t) + C1I, we study the chaos property of the noncommutative L-2 -space with respect to the vacuum expectation tau. Next, we determine the distribution of the q-Levy-Meixner operator < J(chi(D)) = omega, chi(D)> and as a consequence we give some useful properties of the q-Levy-Meixner white noise process.