Title :

Quantitative equidistribution properties of toral eigenfunctions

Author(s) :

Hezari, Hamid [Auteur]
Department of Mathematics [Irvine]
Riviere, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Spectral Theory

Publisher :

European Mathematical Society

Publication date :

2017-06-05

ISSN :

1664-039X

English keyword(s) :

Quantum ergodicity
Eigenfunctions of the Laplacian

HAL domain(s) :

Mathématiques [math]/Théorie spectrale [math.SP]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Physique mathématique [math-ph]

English abstract : [en]

In this note, we prove quantitative equidistribution properties for orthonor-mal bases of eigenfunctions of the Laplacian on the rational d-torus. We show that the rate of equidistribution of such eigenfunctions is polynomial. ...
Show more >In this note, we prove quantitative equidistribution properties for orthonor-mal bases of eigenfunctions of the Laplacian on the rational d-torus. We show that the rate of equidistribution of such eigenfunctions is polynomial. We also prove that equidistribution of eigenfunctions holds for symbols supported in balls with a radius shrinking at a polynomial rate.Show less >

Language :

Anglais

Popular science :

Non

Comment :

This article is based on the appendix of our previous preprint: arXiv:1411.4078. We have included improvements and have simplified the proofs (no semiclassical/microlocal analysis background is required).

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL