95-43 Alain Grigis, Fr\'ed\'eric Klopp.

Valeurs propres et r\'esonances au voisinage d'un seuil. (54K, AMSTeX) Feb 11, 95

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Abstract. In an abstract setting, we consider an operator whose resolvent can be extended meromorphically to a Riemann surface near a branching point. The operator depends on a parameter, and we study the behavior of the resonances i.e. poles of the resolvent as functions of the parameter; in particular, we study what happens when a resonance is located at the branching point. This study may be applied to a periodic Schr\"odinger operator perturbed by a compactly supported potential. The parameter is a coupling constant and the branching point is an edge of the absolutely continuous spectrum of the periodic operator. Remark: the paper is written in french.

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