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Analyse spectrale du modele de Friedrichs. On reduit l'etude du spectre a celles des racines d'une fonction operateur analytique avec la partie imaginaire positive. On donne des theoremes d'unicite pour des fonctions operateurs analytiques a partie imaginaire positive sur le cercle ou le demi-plan. On etudie en detail les racines la fonction operateur M(λ)

Uniqueness theorems for operator-valued functions with positive imaginary part, and the singular spectrum in the selfadjoint Friedrichs model