General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators
Jean DolbeaultUniversité de Paris Dauphine, France
Maria J. EstebanUniversité de Paris Dauphine, France
Éric SéréUniversité de Paris Dauphine, France
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.
Cite this article
Jean Dolbeault, Maria J. Esteban, Éric Séré, General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators. J. Eur. Math. Soc. 8 (2006), no. 2, pp. 243–251DOI 10.4171/JEMS/50