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Renormalized oscillation theory
for Dirac operators

Author: Gerald Teschl
Journal: Proc. Amer. Math. Soc. 126 (1998), 1685-1695
MSC (1991): Primary 34C10, 39L40; Secondary 34B24, 34L15
MathSciNet review: 1443411
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Abstract: Oscillation theory for one-dimensional Dirac operators with separated boundary conditions is investigated. Our main theorem reads: If $\lambda _{0,1}\in \mathbb R$ and if $u,v$ solve the Dirac equation $H u= \lambda _0 u$, $H v= \lambda _1 v$ (in the weak sense) and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection $P_{(\lambda _0, \lambda _1)}(H)$ equals the number of zeros of the Wronskian of $u$ and $v$. As an application we establish finiteness of the number of eigenvalues in essential spectral gaps of perturbed periodic Dirac operators.

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Additional Information

Gerald Teschl
Affiliation: Institut für Reine und Angewandte Mathematik RWTH Aachen 52056 Aachen Germany
Address at time of publication: Institut für Mathematik, Universität Wien, Strudelhofgasse 4, 1090 Vienna, Austria

Keywords: Oscillation theory, Dirac operators, spectral theory
Received by editor(s): November 7, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 by the author