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Article Dans Une Revue international mathematical research notices Année : 2021

The constant term of tempered functions on a real spherical space

Résumé

Let $Z$ be a unimodular real spherical space. We develop a theory of constant terms for tempered functions on $Z$ which parallels the work of Harish-Chandra. The constant terms $f_I$ of an eigenfunction $f$ are parametrized by subsets $I$ of the set $S$ of spherical roots which determine the fine geometry of $Z$ at infinity. Constant terms are transitive i.e. $(f_J)_I=f_I$ for $I\subset J$, and our main result is a quantitative bound of the difference $f-f_I$, which is uniform in the parameter of the eigenfunction.

Dates et versions

hal-02150715 , version 1 (07-06-2019)

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Raphaël Beuzart-Plessis, Patrick Delorme, Bernhard Krötz, Sofiane Souaifi. The constant term of tempered functions on a real spherical space. international mathematical research notices, In press, ⟨10.1093/imrn/rnaa395⟩. ⟨hal-02150715⟩
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