Towards semi-classical analysis for sub-elliptic operators

TL;DR

This paper reviews recent advances in semi-classical and micro-local analysis for sub-elliptic operators on nilpotent Lie groups, focusing on pseudo-differential calculi and quantum limits.

Contribution

It provides an overview of new pseudo-differential calculi and the concept of quantum limits in the context of nilpotent Lie groups and sub-elliptic operators.

Findings

Development of pseudo-differential calculi on nilpotent Lie groups

Analysis of quantum limits in Euclidean and nilpotent settings

Advancements in semi-classical analysis techniques 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.