English

Spectral asymptotics for first order systems

Spectral Theory 2016-12-13 v2

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.

Keywords

Cite

@article{arxiv.1512.06281,
  title  = {Spectral asymptotics for first order systems},
  author = {Zhirayr Avetisyan and Yan-Long Fang and Dmitri Vassiliev},
  journal= {arXiv preprint arXiv:1512.06281},
  year   = {2016}
}

Comments

Edited in accordance with referee's recommendations

R2 v1 2026-06-22T12:14:06.727Z