1409.1869v2.pdf (158.69 kB)
Riesz means of the counting function of the Laplace operator on compact manifolds of non-positive curvature
journal contribution
posted on 2016-01-14, 13:33 authored by Kamil Mroz, Alexander StrohmaierLet (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
6Issue
3Pages
629-642Citation
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 HouseVersion
- 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
2016-09-15Copyright date
2016Notes
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.pdfISSN
1664-039XPublisher version
Language
- en