QUASIANALYTIC FUNCTION CLASSES AND THE COMPLEX-TIME DIFFUSION GROUP - I

In this paper necessary and sufficient conditions are given for quasianalytic function classes D({M_k}) and the corresponding classes of distributions D′({M_k}) to be invariant with respect to the diffusion group U_t where −∞0 denotes the δ-function at 0. It is shown that hyperdistributions Γ from the class D′({M_k}) are completely characterized by the rate of decay of the moments μ_k(Γ) = Γ(x^k), k≥0.