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

• Autores: Jean Dolbeault , María Jesús Esteban-Parra , Eric Séré
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 8, Nº 2, 2006, págs. 243-251
• Idioma: inglés
• DOI: 10.4171/jems/50
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• Resumen

  • 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.