The local counting function of operators of Dirac and Laplace type
journal contributionposted on 2016-01-14, 11:41 authored by Liangpan Li, Alexander Strohmaier
Let P be a non-negative self-adjoint Laplace type operator acting on sections of a hermitian vector bundle over a closed Riemannian manifold. In this paper we review the close relations between various P-related coefficients such as the mollified spectral counting coefficients, the heat trace coefficients, the resolvent trace coefficients, the residues of the spectral zeta function as well as certain Wodzicki residues. We then use the Wodzicki residue to obtain results about the local counting function of operators of Dirac and Laplace type. In particular, we express the second term of the mollified spectral counting function of Dirac type operators in terms of geometric quantities and characterize those Dirac type operators for which this coefficient vanishes.
- Mathematical Sciences
CitationLI, L. and STROHMAIER, A., 2016. The local counting function of operators of Dirac and Laplace type. Journal of Geometry and Physics, 104, pp. 204-228.
- AM (Accepted Manuscript)
Publisher statementThis 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/
NotesThis paper was accepted for publication in the journal Journal of Geometry and Physics and the definitive published version is available at http://dx.doi.org/10.1016/j.geomphys.2016.02.006