Journal of the European Mathematical Society


Full-Text PDF (144 KB) | Table of Contents | JEMS summary
Volume 8, Issue 2, 2006, pp. 243–251
DOI: 10.4171/JEMS/50

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

Jean Dolbeault[1], Maria J. Esteban[2] and Eric Séré[3]

(1) CEREMADE, Université de Paris Dauphine, Place du Marechal de Lattre de Tassigny, 75775, PARIS CEDEX 16, FRANCE
(2) CEREMADE, Université de Paris Dauphine, Place du Marechal de Lattre de Tassigny, 75775, PARIS CEDEX 16, FRANCE
(3) CEREMADE, Université de Paris Dauphine, Place du Marechal de Lattre de Tassigny, 75775, PARIS CEDEX 16, 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.

No keywords available for this article.

Dolbeault J, Esteban M, Séré E. 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), 243-251. doi: 10.4171/JEMS/50