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arXiv · 2507.02469

On the rate of exponential decay of coefficients on homogeneous spaces

Yves Benoist·Siwei Liang
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Abstract

For any homogeneous space of a noncompact semisimple Lie group $G$, we define an exponent with multiple interpretations from representation theory and group theory. As an application, we give a temperedness criterion for $L^2 (G/H)$ for any closed subgroup $H$ of $G$, which extends the existing ones of Benoist--Kobayashi for connected subgroups and Lutsko--Weich--Wolf for discrete subgroups.

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Yves Benoist, Siwei Liang. 2025-12-02. On the rate of exponential decay of coefficients on homogeneous spaces. https://arxiv.org/abs/2507.02469

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