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Spectral asymptotics for first order systems

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. Green open access

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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
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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