Journal of Spectral Theory


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Volume 7, Issue 2, 2017, pp. 471–485
DOI: 10.4171/JST/169

Published online: 2017-06-05

Quantitative equidistribution properties of toral eigenfunctions

Hamid Hezari[1] and Gabriel Rivière[2]

(1) University of California, Irvine, USA
(2) Université Lille 1, Villeneuve d’Ascq, France

In this note, we prove quantitative equidistribution properties for orthonormal bases of eigenfunctions of the Laplacian on the rational $d$-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: Eigenfunctions of the Laplacian, quantum ergodicity, Weyl law, Birkhoff theorem

Hezari Hamid, Rivière Gabriel: Quantitative equidistribution properties of toral eigenfunctions. J. Spectr. Theory 7 (2017), 471-485. doi: 10.4171/JST/169