Geodesic
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, Tome 8 (2006) no. 2, pp. 243-251
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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.
DOI : 10.4171/jems/50
Classification : 47-XX, 81-XX, 00-XX
Keywords: 
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     author = {Jean Dolbeault and Maria J. Esteban and \'Eric S\'er\'e},
     title = {General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. {Application} to {Dirac} operators},
     journal = {Journal of the European Mathematical Society},
     pages = {243--251},
     year = {2006},
     volume = {8},
     number = {2},
     doi = {10.4171/jems/50},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/50/}
}
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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. Journal of the European Mathematical Society, Tome 8 (2006) no. 2, pp. 243-251. doi: 10.4171/jems/50

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