We obtain a representation of the derivative of the spectral shift function $\xi(\lambda,h)$ in the framework of semiclassical "black box" perturbations. Our representation implies a meromorphic continuation of $\xi(\lambda,h)$ involving the semiclassical resonances. Moreover, we obtain a Weyl-type asymptotics of the spectral shift function, as well as a Breit-Wigner approximation in an interval $(\lambda -\delta,\lambda+\delta), 0<\delta<\epsilon h$.
"Meromorphic continuation of the spectral shift function." Duke Math. J. 116 (3) 389 - 430, 15 February 2003. https://doi.org/10.1215/S0012-7094-03-11631-2