Abstract：

We prove an estimate for spherical functions $\varphi_\lambda(a)$ on SL(3,R), establishing uniform decay in the spectral parameter $\lambda$ when the group variable $a$ is restricted to a compact subset of the abelian subgroup $A$. In the case of SL(3,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 $\lambda$ and $a$ vary.

报告人简介：

李晓承2021年9月入职北京大学北京国际数学研究中心博士后，导师为余君教授。2015年7月至2021年5月在美国威斯康星大学麦迪逊分校攻读博士学位，导师为Simon Marshall教授。目前的主要研究兴趣是调和分析与李群。

组织者：张城