Meromorphic continuation of the spectral shift function (Q1395917)

The goal of this paper is to obtain a meromorphic continuation of the derivative of the spectral shift function \(\xi(\lambda,h)\). The authors obtain a representation which implies that a meromorphic continuation of \(\xi(\lambda, h)\) involves the semiclassical resonances. Moreover, they establish a Weyl-type asymptotics of the spectral shift function in the general framework of semiclassical ``black box'' perturbations, improving their previous result and working without assumption on the behaviour of the resonances close to the real axis. Based on the Weyl-type asymptotics the authors present a new, direct, and short proof of the Breit-Wigner approximation in the long-range case.