# An estimate for spherical functions on $\mathrm{SL}(3,\mathbb{R})$

24 Oct 2019 Li Xiaocheng

We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C... (read more)

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# Categories

• REPRESENTATION THEORY
• DIFFERENTIAL GEOMETRY