Quantitative equidistribution properties of toral eigenfunctions
Analysis of PDEs
2015-03-11 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
We prove quantitative equidistribution properties for orthonormal bases of eigenfunctions of the Laplacian on the rational -torus. We show that the rate of equidistribution of such eigenfunctions is of polynomial decay. We also prove that equidistribution of eigenfunctions holds for symbols supported in balls with a radius shrinking at a polynomial rate.
Keywords
Cite
@article{arxiv.1503.02794,
title = {Quantitative equidistribution properties of toral eigenfunctions},
author = {Hamid Hezari and Gabriel Riviere},
journal= {arXiv preprint arXiv:1503.02794},
year = {2015}
}
Comments
This article is based on the appendix of our previous preprint: arXiv:1411.4078. We have included improvements and have simplified the proofs (no semiclassical/microlocal techniques are necessary)