General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators. - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of the European Mathematical Society Année : 2006

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

Résumé

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.
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Dates et versions

hal-00012837 , version 1 (28-10-2005)

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Jean Dolbeault, Maria J. Esteban, Eric Séré. General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators.. Journal of the European Mathematical Society, 2006, 8 (2), pp.243-251. ⟨hal-00012837⟩
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