Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt
Scattering matrices and Weyl functions
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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 
Krein-Birman formula is given. The results are applied to singular 
Sturm-Liouville operators with scalar and matrix potentials, to 
Dirac operators and to Schr\"odinger operators with point 
interactions.