Vincent Bruneau, Vesselin Petkov
Meromorphic continuation of the Spectral Shift Function.
(109K, Latex 2e)
ABSTRACT. We obtain a representation of the derivative of the spectral shift
function $\xi(\lambda, h)$ in the framework of semi-classical
"black box" perturbations. Our representation implies a meromorphic
continuation of $\xi(\lambda, h)$ involving the semi-classical
resonances. Moreover, we obtain a Weyl type asymptotics of the
spectral shift function as well as a Breit-Wigner approximation in an
interval
$(\lambda - \delta, \lambda + \delta), \:\: 0 < \delta < \epsilon h.$