Minimax principles, Hardy-Dirac inequalities, and operator cores for two and three dimensional Coulomb-Dirac operators

  • David Müller

Minimax principles, Hardy-Dirac inequalities, and operator cores for two and three dimensional Coulomb-Dirac operators cover
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Abstract

For we prove minimax characterisations of eigenvalues in the gap of the dimensional Dirac operator with an potential, which may have a Coulomb singularity with a coupling constant up to the critical value . This result implies a so-called Hardy-Dirac inequality, which can be used to define a distinguished self-adjoint extension of the Coulomb-Dirac operator defined on , as long as the coupling constant does not exceed . We also find an explicit description of an operator core of this operator.

Cite this article

David Müller, Minimax principles, Hardy-Dirac inequalities, and operator cores for two and three dimensional Coulomb-Dirac operators. Doc. Math. 21 (2016), pp. 1151–1169

DOI 10.4171/DM/554