Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law |
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| Authors: | Dmitry Jakobson Iosif Polterovich |
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| Institution: | (1) Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Str. West, Montréal, QC, H3A 2K6, Canada;(2) Département de mathématiques et de statistique, Université de Montréal, succ Centre-Ville, Montréal, QC, CP 6128 H3C 3J7, Canada |
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| Abstract: | We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on
manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of
the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and
extend the unpublished thesis of A. Karnaukh Ka].
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.
Received: April 2006 Revision: October 2006 Accepted: October 2006 |
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| Keywords: | Spectral function wave kernel Weyl’ s law Anosov flow |
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