The q-Gamma White Noise

Abstract

For $0<q<1$ and $\alpha < 0$, we construct the infinite dimensional $q$-Gamma white noise measure $\gamma_{\alpha, q}$ by using Bockner-Minlos theorem. Then we give the chaos decomposition of an $L^{2}$ space with respect to the measure $\gamma_{\alpha, q}$ via an isomorphism with 1-mode type interacting Fock space associated to the q -Gamma measure.