Contents 0 Introduction 2 1 Notations and preliminaries 5 2 Invariant diierential operators 9 3 Deenition of the Eisenstein integral 13 4 Relation with the principal series 14 5 Finite dimensional class (1,1) representations 20 6 Functions of S-polynomial growth 23 7 S-genericity 25 8 Projection along innnitesimal characters 25 9 Estimates for j 30 10 Initial estimates for Eisenstein integrals ...