Fonctions généralisées sphériques induites sur G_C/G_R et applications

Let G be a complex semisimple Lie group with Lie algebra g. Let h be a real form of g and let H be the analytic subgroup of G with Lie algebra h. By induction, we construct a spherical generalized function p - ind^G_Lθ from a spherical generalized function θ defined on a smaller symmetric space L L ∩ H. When θ is the coefficient of a representation, we prove that p - ind^G_Lθ is a coefficient of a representation induced from a parabolic subgroup. Applying these results to the space GL(n, C)/GL(n, R) we obtain the Plancherel formula for this space from the inversion formula proved by S. Sano.