01-484 Mouez Dimassi, Maher Zerzeri

A LOCAL TRACE FORMULA FOR RESONANCES OF PERTURBED PERIODIC SCHR\"ODINGER OPERATORS (242K, Postscript) Dec 21, 01

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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 $\scriptstyle\sigma(P_0).$

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