Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds

TL;DR

This paper extends semiclassical calculus to nilpotent Lie groups and nilmanifolds, including subelliptic operators, and establishes Weyl laws for their spectral properties.

Contribution

It introduces a semiclassical functional calculus for subelliptic operators on nilpotent Lie groups and nilmanifolds, and derives Weyl laws for these operators.

Findings

Semiclassical calculus includes subelliptic operators on nilpotent groups.

Weyl laws are established for these operators.

Results apply to sub-Laplacians with potentials and their generalizations.

Abstract

In this paper, we show that the semiclassical calculus recently developed on nilpotent Lie groups and nilmanifolds include the functional calculus of suitable subelliptic operators. Moreover, we obtain Weyl laws for these operators. Amongst these operators are sub-Laplacians in horizontal divergence form perturbed with a potential and their generalisations.