Vincent Bruneau, Vesselin Petkov
Representation of the spectral shift function and spectral asymptotics for trapping perturbations
(96K, Latex 2e)

ABSTRACT.  We obtain in the semi-classical setup of "black box" long-range perturbations a representation for the derivative of spectral shift function $\xi(\lambda)$ related to two self-adjoint operators $L_j(h), \: j = 1,2. $ We show that the derivative $\xi'(\lambda)$ is estimated by the norms of the cut-off resolvents of the operators $L_j(h)$. Finally, we establish a Weyl type formula for the spectral shift function $\xi(\lambda)$ generalizing the results of Robert [R94] and Christiansen [Ch98].