Fonctions D(G/H)-Finies sur un Espace Symétrique Réductif

It is well known that, on Rn, every smooth function annihilated by a finite codimensional ideal in the algebra of constant coefficient differential operators, is a linear combination of polynomial exponential functions, P(x)eλ(x), λ ∈ Hom(Rn,C). Furthermore, the polynomial functions are obtained by applying to the exponential functions eλ(x) some constant coefficient differential operator in the parameter λ. We generalize this fact to the reductive symmetric spacesʹ case, the role of the exponential functions being taken by the Eisenstein integrals.