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arXiv · 1503.02794

Quantitative equidistribution properties of toral eigenfunctions

Hamid Hezari·Gabriel Riviere
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Abstract

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.

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Hamid Hezari, Gabriel Riviere. 2015-03-10. Quantitative equidistribution properties of toral eigenfunctions. https://arxiv.org/abs/1503.02794

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