Avetisyan, Zhirayr; Fang, Yan-Long; Vassiliev, Dmitri Spectral asymptotics for first order systems. (English) Zbl 1423.35281 J. Spectr. Theory 6, No. 4, 695-715 (2016). Summary: 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. Cited in 5 Documents MSC: 35P20 Asymptotic distributions of eigenvalues in context of PDEs 35J46 First-order elliptic systems 35Q41 Time-dependent Schrödinger equations and Dirac equations 35R01 PDEs on manifolds 58J50 Spectral problems; spectral geometry; scattering theory on manifolds Keywords:spectral theory; Weyl asymptotics; Dirac operator; spectral asymmetry PDFBibTeX XMLCite \textit{Z. Avetisyan} et al., J. Spectr. Theory 6, No. 4, 695--715 (2016; Zbl 1423.35281) Full Text: DOI arXiv References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.