Avetisyan, Z;
Fang, Y-L;
Vassiliev, D;
(2016)
Spectral asymptotics for first order systems.
Journal of Spectral Theory
, 6
(4)
pp. 695-715.
10.4171/JST/137.
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Abstract
This is a review paper outlining recent progress in the spectral analysis of first order systems. We work on a closed manifold and study an elliptic self-adjoint first order system of linear partial differential equations. The aim is to examine the spectrum and derive asymptotic formulae for the two counting functions. Here the two counting functions are those for the positive and the negative eigenvalues. One has to deal with positive and negative eigenvalues separately because the spectrum is, generically, asymmetric.
Type: | Article |
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Title: | Spectral asymptotics for first order systems |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.4171/JST/137 |
Publisher version: | http://dx.doi.org/10.4171/JST/137 |
Language: | English |
Additional information: | This is a manuscript version of an article accepted for publication in the Journal of Spectral Theory: http://www.ems-ph.org/journals/journal.php?jrn=jst. |
Keywords: | Spectral theory, Weyl asymptotics, Dirac operator, spectral asymmetry |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
URI: | https://discovery.ucl.ac.uk/id/eprint/1481467 |
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