The q-Gamma White Noise

For 0 < q < 1 and 0 < α < 1, we construct the infinite dimensional q-Gamma white noise measure γ_α,q by using the Bochner-Minlos theorem. Then we give the chaos decomposition of an L² space with respect to the measure γ_α,q via an isomorphism with the 1-mode type interacting Fock space associated to the q-Gamma measure.