Fractional Gamma Noise Functionals

We construct an infinite dimensional analysis with respect to non-Gaussian measures of fractional Gamma type which we call fractional Gamma noise measures. It turns out that the well-known Wick ordered polynomials in Gaussian analysis cannot be generalized to this non-Gaussian case. Instead of using generalized Appell polynomials we prove that a system of biorthogonal polynomials, called Appell system, is applicable to the fractional Gamma measures. Finally, we gives some new properties of the kernels expressed in terms of the Stirling operators of the first and second kind as well as the falling factorials in infinite dimensions and we construct the so-called fractional Gamma noise Gel’fand triple.