 06109 Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt
 Scattering matrices and Weyl functions
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Apr 7, 06

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Abstract. For a scattering system $\{A_\Theta,A_0\}$ consisting of
selfadjoint extensions $A_\Theta$ and $A_0$ of a symmetric operator
$A$ with finite deficiency indices, the scattering matrix
$\{S_\Theta(\gl)\}$ and a spectral shift function
$\xi_\Theta$ are calculated in terms of the Weyl function associated
with the boundary triplet for $A^*$ and a simple proof of the
KreinBirman formula is given. The results are applied to singular
SturmLiouville operators with scalar and matrix potentials, to
Dirac operators and to Schr\"odinger operators with point
interactions.
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