JournalsjemsVol. 8, No. 2pp. 243–251

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

  • Jean Dolbeault

    Université de Paris Dauphine, France
  • Maria J. Esteban

    Université de Paris Dauphine, France
  • Éric Séré

    Université de Paris Dauphine, France
General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators cover
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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.

Cite this article

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. J. Eur. Math. Soc. 8 (2006), no. 2, pp. 243–251

DOI 10.4171/JEMS/50