Multilinear estimates for the Laplace spectral projectors on compact manifolds

Nicolas Burq; Patrick Gérard; Nikolay Tzvetkov

doi:10.1016/j.crma.2003.12.015

Mathematical Analysis/Partial Differential Equations

Multilinear estimates for the Laplace spectral projectors on compact manifolds

Presented by: Yves Meyer

Nicolas Burq ¹; Patrick Gérard ¹; Nikolay Tzvetkov ¹

¹ Université Paris Sud, mathématiques, bâtiment 425, 91405 Orsay cedex, France

Comptes Rendus. Mathématique, Volume 338 (2004) no. 5, pp. 359-364.

Abstract
Résumé

The purpose of this Note is to extend to any space dimension the bilinear estimate for eigenfunctions of the Laplace operator on a compact manifold (without boundary) obtained by the authors (preprint: http://www.arxiv.org/abs/math/0308214) in dimension 2. We also give some related trilinear estimates.

L'objet de cette Note est de généraliser à toute dimension d'espace les estimations bilinéaires de projecteurs spectraux de l'opérateur de Laplace sur une variété compacte (sans bord), démontrées par les auteurs (preprint : http://www.arxiv.org/abs/math/0308214) en dimension 2. On énonce aussi des estimations trilinéaires.

Received: 2003-10-07
Accepted: 2003-12-02
Published online: 2004-01-29

DOI: 10.1016/j.crma.2003.12.015

Author's affiliations:

Nicolas Burq ¹; Patrick Gérard ¹; Nikolay Tzvetkov ¹

¹ Université Paris Sud, mathématiques, bâtiment 425, 91405 Orsay cedex, France

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     author = {Nicolas Burq and Patrick G\'erard and Nikolay Tzvetkov},
     title = {Multilinear estimates for the {Laplace} spectral projectors on~compact manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {359--364},
     publisher = {Elsevier},
     volume = {338},
     number = {5},
     year = {2004},
     doi = {10.1016/j.crma.2003.12.015},
     language = {en},
}

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Nicolas Burq; Patrick Gérard; Nikolay Tzvetkov. Multilinear estimates for the Laplace spectral projectors on compact manifolds. Comptes Rendus. Mathématique, Volume 338 (2004) no. 5, pp. 359-364. doi : 10.1016/j.crma.2003.12.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.12.015/

References
Cited by

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[7] E.M. Stein Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Monographs Harmon. Anal., III, Princeton University Press, Princeton, NJ, 1993

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