Quantitative equidistribution properties of toral eigenfunctions
Hamid Hezari
University of California, Irvine, USAGabriel Rivière
Université Lille 1, Villeneuve d’Ascq, France
![Quantitative equidistribution properties of toral eigenfunctions cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jst-volume-7-issue-2.png&w=3840&q=90)
Abstract
In this note, 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.
Cite this article
Hamid Hezari, Gabriel Rivière, Quantitative equidistribution properties of toral eigenfunctions. J. Spectr. Theory 7 (2017), no. 2, pp. 471–485
DOI 10.4171/JST/169