The constant term of tempered functions on a real spherical space
Résumé
Let Z be a unimodular real spherical space which is assumed of wave-front type. Generalizing some ideas of Harish-Chandra [5, 6], we show the existence of the constant term for smooth tempered functions on Z, while Harish-Chandra dealt with K-finite functions on the group (see also the work of Wallach [16, Chapter 12], dealing with smooth functions on the group and using asymptotic expansions). By applying this theory, we get a characterization of the relative discrete series for Z. Some features for the constant term, namely transitivity and uniform estimates, are also established.
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