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Soit Γ un sous-groupe discret d'automorphismes de H n , a polyedre fondamental de volume fini, de nombre de cotes fini et a n cusps, soit Δ Γ l'operateur de Laplace-Beltrami agissant sur des fonctions automorphes par rapport a Γ. On demontre que Δ Γ a un spectre absolument continu de multiplicite uniforme N sur (−∞,((n-1)/2 2 ), plus un spectre standard discret

Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces; the case of finite volume