02-509 Bouclet J-M

Traces formulae for relatively Hilbert-Schmidt perturbations (457K, Postscript) Dec 9, 02

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Abstract. The main goal of this paper is to introduce tools able to replace Krein's spectral shift function when it cannot be defined. We introduce a function $\eta$ for a class of perturbation of pseudodifferential operators on ${\mathbb R}^d$ when these perturbations decay as $<x>^{-\rho}$, $\rho > d /2$, at infinity. In euclidean scattering, we establish a complete asymptotic expansion for $\eta$, under the usual non trapping assumption and we deduce a Levinson formula for the Schr\"odinger operator on ${\mathbb R}^3$. Some results on the general case are also given.

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