Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds

Véronique Fischer; Søren Mikkelsen

doi:10.1007/s13324-025-01051-z

Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds

Véronique Fischer, Søren Mikkelsen

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	60
Journal	Analysis and Mathematical Physics
Volume	15
Issue number	3
Early online date	24 Apr 2025
DOIs	https://doi.org/10.1007/s13324-025-01051-z
Publication status	E-pub ahead of print - 24 Apr 2025

Data Availability Statement

No datasets were generated or analysed during the current study.

Acknowledgements

We also thank Lino Benedetto for interesting discussions and references.

Funding

The authors are grateful to the Leverhulme Trust for their support via Research Project Grant 2020-037.

Keywords

Harmonic and functional analysis on nilpotent Lie groups and nilmanifolds
Semiclassical analysis

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics

Access to Document

10.1007/s13324-025-01051-zLicence: CC BY

Cite this

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Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds

Abstract

Data Availability Statement

Acknowledgements

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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