Bouclet J-M
Traces formulae for relatively Hilbert-Schmidt perturbations
(457K, Postscript)

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.