Journal of Spectral Theory
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Published online: 2017-06-05
Quantitative equidistribution properties of toral eigenfunctionsHamid Hezari and Gabriel Rivière (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