On the Ornstein-Uhlenbeck operator in spaces of continuous functions (Q1908150): Difference between revisions

The authors study the realization of the Ornstein-Uhlenbeck operator \({\mathcal A}\) in the space of the uniform continuous and bounded functions in \(\mathbb{R}^n\). They prove that it generates a semigroup which is neither strongly continuous nor analytic, but enjoys nice smoothing properties. Such properties are used to prove a Schauder-type theorem for the elliptic equation \(\lambda u- {\mathcal A} u=f\).