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Riesz means of the counting function of the Laplace operator on compact manifolds of non-positive curvature

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posted on 14.01.2016, 13:33 by Kamil Mroz, Alexander Strohmaier
Let (M, g) be a compact, d-dimensional Riemannian manifold without boundary. Suppose further that (M, g) is either two dimensional and has no conjugate points or (M, g) has non-positive sectional curvature. The goal of this note is to show that the long time parametrix obtained for such manifolds by B´erard can be used to prove a logarithmic improvement for the remainder term of the Riesz means of the counting function of the Laplace operator.

History

School

  • Science

Department

  • Mathematical Sciences

Volume

6

Issue

3

Pages

629-642

Citation

MROZ, K. and STROHMAIER, A., 2016. Riesz means of the counting function of the Laplace operator on compact manifolds of non-positive curvature. Journal of Spectral Theory, 6 (3), pp.629-642.

Publisher

© EMS Publishing House

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2016-09-15

Copyright date

2016

Notes

This paper was accepted for publication in the Journal of Spectral Theory and the accepted version is also available in arXiv http://arxiv.org/pdf/1409.1869v2.pdf

ISSN

1664-039X

Language

en

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