- 05-396 Jean DOLBEAULT, Maria J. ESTEBAN, Eric SERE
- General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators.
Nov 20, 05
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Abstract. 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.