报告人：张城（清华大学）

邀请人：黄山林

报告时间：2023年10月26日（星期四）10:00-12:00

报告地点：腾讯会议：170 443 071

报告题目：Sharp Local L^p estimates for the Hermite eigenfunctions

报告摘要：We investigate the concentration of eigenfunctions for the Hermite operator $-\Delta+|x|^2$ in $\mathbb{R}^n$ by establishing new $L^p$ bounds over compact sets. Compared to Koch-Tataru's global estimates, these new estimates demonstrate local improvements for a certain range of $p$. The sharpness of these local estimates can be verified by examples with various types of concentrations. Moreover, we prove that the sharp $L^p$ bounds of the Hermite eigenfunctions over fixed compact sets coincide with Sogge's $L^p$ bounds for the Laplace eigenfunctions on compact manifolds, up to a scaling factor $\lambda^{-\frac12}$. This  phenomenon suggests that the Hermite eigenfunctions locally resemble the rescaled Laplace eigenfunctions. These results strengthen the local estimates by Thangavelu and Koch-Tataru.

报告人简介：张城博士，清华大学数学中心助理教授。2014年本科毕业于浙江大学，2019年博士毕业于美国约翰霍普金斯大学。研究方向是调和分析及其应用，主要研究流形上的特征值与特征函数问题，获得国家海外高层次人才项目和国家自然科学基金委面上项目资助。