  We introduce the Riesz operator in the context of Gromov hyperbolic groups in
order to investigate a one parameter family of non unitary boundary Hilbertian
representations of hyperbolic groups. We prove asymptotic Schur's relations,
the latter being the main result of this paper. Up to normalization, the Riesz
operator plays the role in the context of hyperbolic groups of the Knapp-Stein
intertwiner for complementary series for Lie groups. Assuming the positivity of
the Riesz operator, we define an analogue of complementary series for
hyperbolic groups and prove their irreducibility.
