Geometric invariance of the semi-classical calculus on nilpotent graded Lie groups
Functional Analysis
2023-04-04 v2 Differential Geometry
Abstract
In this paper, we consider the semi-classical setting constructed on nilpotent graded Lie groups by means of representation theory. We analyze the effects of the pull-back by diffeomorphisms on pseudodifferential operators. We restrict to diffeomorphisms that preserve the filtration and prove that they are Pansu differentiable. We show that the pull-back of a semi-classical pseudodifferential operator by such a diffeomorphism has a semi-classical symbol that is expressed at leading order in terms of the Pansu differential. We interpret the geometric meaning of this invariance in the setting of filtered manifolds.
Keywords
Cite
@article{arxiv.2112.11509,
title = {Geometric invariance of the semi-classical calculus on nilpotent graded Lie groups},
author = {Clotilde Fermanian Kammerer and Veronique Fischer and Steven Flynn},
journal= {arXiv preprint arXiv:2112.11509},
year = {2023}
}
Comments
25 pages