Mouez Dimassi, Maher Zerzeri
A LOCAL TRACE FORMULA FOR RESONANCES OF PERTURBED PERIODIC SCHR\"ODINGER OPERATORS
(242K, Postscript)

ABSTRACT.  We give a local trace formula for the pair 
$\scriptstyle 
(P_1(h)=P_0+W(h y),\ P_0),$ where $\scriptstyle 
P_0$ is a periodic Schr\"odinger 
operator, $\scriptstyle W$ is a decreasing perturbation and 
$\scriptstyle h$ is a small positive parameter. 
We apply this result to establish the existence 
of $\ \scriptstyle\sim h^{-n}$ resonances near some energy 
$\scriptstyle\lambda$ of 
$\scriptstyle\sigma(P_0).$