English

General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators

Analysis of PDEs 2023-11-06 v1 Mathematical Physics math.MP

Abstract

This paper is concerned with {an extension and reinterpretation} of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. {We state} two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then, these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.

Keywords

Cite

@article{arxiv.math/0510626,
  title  = {General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators},
  author = {Jean Dolbeault and Maria J. Esteban and Eric séré},
  journal= {arXiv preprint arXiv:math/0510626},
  year   = {2023}
}