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Weak convergence of spectral shift functions revisited
We study convergence of the spectral shift function for the finite interval
restrictions of a pair of full-line Schr\"odinger operators to an interval of
the form with coupled boundary conditions at the endpoints as
in the case when the finite interval restrictions are
relatively prime to those with Dirichlet boundary conditions. Using a
Krein-type resolvent identity we show that the spectral shift function for the
finite interval restrictions converges weakly to that for the pair of full-line
Schr\"odinger operators as the length of the interval tends to infinity.Comment: 23 page