01-332 Vincent Bruneau, Vesselin Petkov

Meromorphic continuation of the Spectral Shift Function. (109K, Latex 2e) Sep 21, 01

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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 $(\lambda - \delta, \lambda + \delta), \:\: 0 < \delta < \epsilon h.$

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