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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Duke Mathematical Journal
( Vol. 116 NO.3 / (2003))
Meromorphic Continuation of the Spectral Shift Function
Vincent Bruneau, Vesselin Petkov,
Pages. 389-430
Abstract 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 $(lambda - delta, lambda + delta), 0 < delta < epsilon h$.
Contents 1. Introduction
2. Preliminaries
3. Representation of the derivative of the spectral shift function
4. Meromorphic continuation of the spectral shift function
5. Weyl asymptotics
6. Breit-Wigner approximation
7. Local trace formula
8. Existence of resanances close to the real axis
Key words
Mathmatical Subject Classification 35P25, 35B34