Regularity results for Kolmogorov equations in $L^2 (H, μ)$ spaces and applications

• Date: 1997
• Main Authors: Da, Prato G., Да, Прато Г.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 1997
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5017
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...