One-side Liouville Theorem for hypoelliptic Ornstein--Uhlenbeck operators having drifts with imaginary spectrum

Alessia E. Kogoj, Ermanno Lanconelli, Giulio Tralli

We prove the Liouville theorem for \emph{non-negative} solutions to (possibly degenerate) Ornstein-Uhlenbeck equations whose linear drift has imaginary spectrum. This provides an a…