Quantitative version of Weyl's law
Analysis of PDEs
2023-03-03 v1 Spectral Theory
Abstract
We prove a general estimate for the Weyl remainder of an elliptic, semiclassical pseudodifferential operator in terms of volumes of recurrence sets for the Hamilton flow of its principal symbol. This quantifies earlier results of Volovoy. Our result particularly improves Weyl remainder exponents for compact Lie groups and surfaces of revolution. And gives a quantitative estimate for B\'erard's Weyl remainder in terms of the maximal expansion rate and topological entropy of the geodesic flow.
Cite
@article{arxiv.2303.01407,
title = {Quantitative version of Weyl's law},
author = {Nikhil Savale},
journal= {arXiv preprint arXiv:2303.01407},
year = {2023}
}