Restriction of toral eigenfunctions to hypersurfaces

Bourgain, Jean; Rudnick, Zeév

doi:10.1016/j.crma.2009.08.008

Partial Differential Equations

Restriction of toral eigenfunctions to hypersurfaces
[Sur la restriction de fonctions propre du tore à des hyper-surfaces]

Présenté par : Jean Bourgain

Bourgain, Jean ¹ ; Rudnick, Zeév ^1,²

¹ School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States
² Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

Comptes Rendus. Mathématique, Tome 347 (2009) no. 21-22, pp. 1249-1253.

Résumé
Abstract

Soit $T^{d} = R^{d} / Z^{d}$ le tore plat d-dimensionnel. Pour $d = 2$ et $d = 3$ , on établit des bornes supérieures et inférieures uniformes sur les restrictions des fonctions propres de l'opérateur de Laplace–Beltrami à des surfaces lisses de courbure non nulle.

Let $T^{d} = R^{d} / Z^{d}$ be the d-dimensional flat torus. We establish for $d = 2, 3$ uniform upper and lower bounds on the restrictions of the eigenfunctions of the Laplacian to smooth hyper-surfaces with non-vanishing curvature.

Reçu le : 2009-07-28
Accepté le : 2009-08-06
Publié le : 2009-10-01

DOI : 10.1016/j.crma.2009.08.008

Affiliations des auteurs :

Bourgain, Jean ¹ ; Rudnick, Zeév ^{1, 2}

¹ School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States
² Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

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Bourgain, Jean; Rudnick, Zeév. Restriction of toral eigenfunctions to hypersurfaces. Comptes Rendus. Mathématique, Tome 347 (2009) no. 21-22, pp. 1249-1253. doi : 10.1016/j.crma.2009.08.008. http://www.numdam.org/articles/10.1016/j.crma.2009.08.008/

Bibliographie
Cité par

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