Towards semi-classical analysis for sub-elliptic operators

Abstract

We discuss the recent developments of semi-classical and micro-local analysis in the context of nilpotent Lie groups and for sub-elliptic operators. In particular, we give an overview of pseudo-differential calculi recently defined on nilpotent Lie groups as well as of the notion of quantum limits in the Euclidean and nilpotent cases.

This paper summarises the main ideas discussed by the author to the Bruno Pini Mathematical Analysis Seminar of the University of Bologna in May 2021