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 L ² 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 $t \in {\mathbb{R}}$.