Ornstein-Uhlenbeck semi-groups on stratified groups

TL;DR

This paper studies two versions of Ornstein-Uhlenbeck semi-groups on stratified groups, focusing on their properties when acting on function spaces with heat kernel invariant measures.

Contribution

It introduces and analyzes two analogues of Ornstein-Uhlenbeck semi-groups on stratified groups, extending classical results to this non-commutative setting.

Findings

Characterization of the semi-groups' properties on stratified groups

Identification of invariant measures as heat kernels

Extension of Ornstein-Uhlenbeck theory to non-commutative groups

Abstract

We consider, in the setting of stratified groups G, two analogues of the Ornstein-Uhlenbeck semi-group, namely Markovian diffusion semi-groups acting on $L^q(pd g)$, whose invariant density $p$ is a heat kernel at time 1 on G.