00-400 Vincent Bruneau, Vesselin Petkov
Representation of the spectral shift function and spectral asymptotics for trapping perturbations (96K, Latex 2e) Oct 9, 00
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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].

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