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- W2978948077 abstract "We prove an estimate for spherical functions $varphi_lambda(a)$ 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. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $lambda$ and $a$ vary." @default.
- W2978948077 created "2019-10-10" @default.
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- W2978948077 date "2019-10-02" @default.
- W2978948077 modified "2023-09-23" @default.
- W2978948077 title "An estimate for spherical functions on $mathrm{SL}(3,mathbb{R})$" @default.
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- W2978948077 doi "https://doi.org/10.48550/arxiv.1910.01048" @default.
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