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ISSN 1079-6762

 

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


Authors: Dmitry Jakobson and Iosif Polterovich
Journal: Electron. Res. Announc. Amer. Math. Soc. 11 (2005), 71-77
MSC (2000): Primary 58J50; Secondary 35P20, 37C30, 81Q50
Published electronically: September 23, 2005
MathSciNet review: 2176067
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Abstract: 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 Our results develop and extend the unpublished thesis of A. Karnaukh.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.


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Additional Information

Dmitry Jakobson
Affiliation: Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montréal QC H3A 2K6, Canada
Email: jakobson@math.mcgill.ca

Iosif Polterovich
Affiliation: Département de mathématiques et de statistique, Université de Montréal CP 6128 Succ. Centre-Ville, Montréal QC H3C 3J7, Canada
Email: iossif@dms.umontreal.ca

DOI: http://dx.doi.org/10.1090/S1079-6762-05-00149-6
PII: S 1079-6762(05)00149-6
Keywords: Weyl's law, spectral function, wave kernel, negative curvature, Anosov flow, thermodynamic formalism
Received by editor(s): June 7, 2005
Published electronically: September 23, 2005
Additional Notes: The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation fellowship and Dawson fellowship. The second author was supported by NSERC and FQRNT
Communicated by: Svetlana Katok
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.