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}
}