Abstract
The main purpose of this paper is to derive a general structure of Gegenbauer white noise analysis as a counterpart class of non-Levy white noise. First, we start with a new detailed construction of the Gegenbauer Fock space Gamma(beta)(H) which serves to obtain the quantum decomposition associated with the Gegenbauer white noise processes. More precisely, based on the notion of quantum decomposition and the orthogonalization of polynomials of noncommutative Gegenbauer white noise omega(t) := b(t)* + b(t) + b(t)*b(t)(b) over tilde (t), 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 Gegenbauer operator J(chi(D)) = (omega, chi(D)) and as a consequence we give some useful properties of the Gegenbauer white noise process.