# The constant term of tempered functions on a real spherical space

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02150715
Contributor : Raphaël Beuzart-Plessis <>
Submitted on : Friday, June 7, 2019 - 1:44:42 PM
Last modification on : Saturday, June 8, 2019 - 1:26:38 AM

### Identifiers

• HAL Id : hal-02150715, version 1
• ARXIV : 1702.04678

### Citation

Raphaël Beuzart-Plessis, Patrick Delorme, Bernhard Krötz, Sofiane Souaifi. The constant term of tempered functions on a real spherical space. 2019. ⟨hal-02150715⟩

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