Weak convergence of spectral shift functions revisited

Abstract

We study convergence of the spectral shift function for the finite interval restrictions of a pair of full-line Schrödinger operators to an interval of the form $(-\ell ,\ell )$ with coupled boundary conditions at the endpoints as $\ell \to \infty$ 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 Schrödinger operators as the length of the interval tends to infinity.

23 pages