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Pré-Publication, Document De Travail Année : 2017

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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Dates et versions

hal-01467990 , version 1 (15-02-2017)

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  • HAL Id : hal-01467990 , version 1

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Patrick Delorme, Bernhard Krötz, Sofiane Souaifi. The constant term of tempered functions on a real spherical space. 2017. ⟨hal-01467990⟩
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