Paquets dʹondes dans lʹespace de Schwartz dʹun espace symétrique réductif

Résumé dy holomorphic families ofK-finite eigenfunctions on symmetric spacesG/H, called functionsIIhol(Λ) by analogy with [HC]. Eisenstein integrals (cf. [B3], [D]), suitably normalized by a polynomial factor, provide examples of such families. A functionIIhol(Λ) is saidII′hol(Λ), if, roughly speaking, its constant term along anyσθ-stable parabolic subgroup is a finite sum of functionsIIhol(Λs), whereΛsvaries in a determined finite set. We prove that, for a functionII′hol(Λ), one can form wave packets in the Schwartz space. We prove also a criterion for a functionIIhol(Λ) to beII′hol(Λ). An important fact is that, for minimalσθ-stable parabolic subgroups, our criterion implies, with the help of the Maas–Selberg relations (cf. [B2], [B3]), a normalization of Eisenstein integrals. All the article relies on the theory of the constant term (cf. [C]).