We define and establish the main properties of the constant term of a tempered m-spherical function F on a non riemannian Symmetrie space, finite under the action of the algebra of the G-invariant differential operators on G JH. Using the theory of asymptotics s developped in [3], [4] and [5], we extend to this case the results of [13] and [3] on the canonical decomposition of the constant term and the meromorphic dependence of the components in the case of a holomorphic family. Estimates are established which are uniform with respect to the parameter in the holomorphic case. Those results can be applied to the Eisenstein integrals studied in [10].
We study holomorphic families of K-finite eigenfunctions on symmetric spaces s varies in a determined finite set. We prove that, for a function II$ hol (4), one can form wave packets in the Schwartz space. We prove also a criterion for a function II hol (4) to be II$ hol (4). An important fact is that, for minimal _%-stable parabolic subgroups, our criterion implies, with the help of the Maas Selberg relations (cf.
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