Regularity results for Kolmogorov equations in L^2 (H, μ) spaces and applications - Da, Prato G. (Ukrains’kyi Matematychnyi Zhurnal, 1997)
We consider the transition semigroup R_t =e^tsA associated to an Ornstein—Uhlenbeck process in a Hilbert space H. We characterize, under suitable assumptions, the domain of A as a subspace W^2,2 (H, μ), where μ is the invariant measure associated to R_t. This characterization is then used to treat some Kolmogorov equations with variable coefficients.