Alain Grigis, Fr\'ed\'eric Klopp.
Valeurs propres et r\'esonances au voisinage d'un seuil.
(54K, AMSTeX)

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.