Estimates from below for the spectral function and for the remainder in local Weyl's law
Spectral Theory
2007-05-23 v3 Differential Geometry
Dynamical Systems
Abstract
We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and extend the unpublished thesis of A. Karnaukh.
Keywords
Cite
@article{arxiv.math/0505400,
title = {Estimates from below for the spectral function and for the remainder in local Weyl's law},
author = {Dmitry Jakobson and Iosif Polterovich},
journal= {arXiv preprint arXiv:math/0505400},
year = {2007}
}
Comments
27 pages. To appear in GAFA