Journal of Spectral Theory

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Volume 6, Issue 4, 2016, pp. 695–715
DOI: 10.4171/JST/137

Published online: 2016-12-09

Spectral asymptotics for first order systems

Zhirayr Avetisyan[1], Yan-Long Fang[2] and Dmitri Vassiliev[3]

(1) University College London, UK
(2) University College London, UK
(3) University College London, UK

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.

Keywords: Spectral theory, Weyl asymptotics, Dirac operator, spectral asymmetry

Avetisyan Zhirayr, Fang Yan-Long, Vassiliev Dmitri: Spectral asymptotics for first order systems. J. Spectr. Theory 6 (2016), 695-715. doi: 10.4171/JST/137