Ornstein–Uhlenbeck operators with time periodic coefficients

Abstract

We study the realization of the differential operator \(u \mapsto u_t - L(t)u\) in the space of continuous time periodic functions, and in L2 with respect to its (unique) invariant measure. Here L(t) is an Ornstein-Uhlenbeck operator in \({\mathbb{R}}^n\), such that L(t + T) = L(t) for each \(t \in {\mathbb{R}}\).