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Journal of the London Mathematical Society 1999 60(2):490-500; doi:10.1112/S0024610799007930
© 1999 by London Mathematical Society
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© The London Mathematical Society

A Minimax Principle for the Eigenvalues in Spectral Gaps

Marcel Griesemer and Heinz Siedentop

Mathematik, Universität Regensburg D-93040 Regensburg, Germany Marcel.Griesemer{at}mathematik.uni-regensburg.de
Mathematik, Universität Regensburg D-93040 Regensburg, Germany Heinz.Siedentop{at}mathematik.uni-regensburg.de

Received 4 December 1997.

A minimax principle is derived for the eigenvalues in the spectral gap of a possibly non-semibounded self-adjoint operator. It allows the nth eigenvalue of the Dirac operator with Coulomb potential from below to be bound by the nth eigenvalue of a semibounded Hamiltonian which is of interest in the context of stability of matter. As a second application it is shown that the Dirac operator with suitable non-positive potential has at least as many discrete eigenvalues as the Schrödinger operator with the same potential.


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