Quantitative equidistribution properties of toral eigenfunctions

  • Hamid Hezari

    University of California, Irvine, USA
  • Gabriel Rivière

    Université Lille 1, Villeneuve d’Ascq, France

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