96-490 Gerald Teschl
Renormalized Oscillation Theory for Dirac Operators (36K, LaTeX2e) Oct 15, 96
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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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