Li, L and Strohmaier, A orcid.org/0000-0002-8446-3840 (2016) The local counting function of operators of Dirac and Laplace type. Journal of Geometry and Physics, 104. C. pp. 204-228. ISSN 0393-0440
Abstract
Let PP 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 PP-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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016, Elsevier. This is an author produced version of a paper published in Journal of Geometry and Physics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Dirac and Laplace type operators;; Spectral zeta and eta functions; Heat traces; Wodzicki residues; Local counting functions |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 Feb 2017 11:59 |
Last Modified: | 23 Jan 2018 08:07 |
Published Version: | https://doi.org/10.1016/j.geomphys.2016.02.006 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.geomphys.2016.02.006 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111662 |