Lower bounds for the spectral function and for the remainder in local Weyl’s law on manifolds

Jakobson, Dmitry¹ ; Polterovich, Iosif²

¹ Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montréal QC H3A 2K6, Canada
² Département de mathématiques et de statistique, Université de Montréal CP 6128 Succ. Centre-Ville, Montréal QC H3C 3J7, Canada

Electronic research announcements of the American Mathematical Society, Tome 11 (2005), pp. 71-77.

Résumé

We announce asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in the local Weyl’s law on Riemannian manifolds. In the negatively curved case, methods of thermodynamic formalism are applied to improve the estimates. Our results develop and extend the unpublished thesis of A. Karnaukh. We discuss some ideas of the proofs; for complete proofs see our extended paper on the subject.

Détail

DOI : 10.1090/S1079-6762-05-00149-6

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