分析和微分方程讨论班——Sharp Spectral-Cluster Restriction Bounds for Orthonormal Systems

报告人：简昌彪（中国工程物理研究院）

时间：2025年7月5日，09:30-10:30

地点：海纳苑2幢203室

摘要:For a smooth $k$-dimensional submanifold $\Sigma$ of a $d$-dimensional compact Riemannian manifold $M$, we will discuss how to extend the $L^p(\Sigma)$ restriction bounds of Burq--Gérard--Tzvetkov \cite{bgt2007}—originally proved for individual Laplace--Beltrami eigenfunctions—to arbitrary systems of $L^2(M)$-orthonormal functions. Our bounds are essentially optimal for every triple $(k,d,p)$ with $p\ge2$, except possibly when $d\ge3,\quad k=d-1,\quad 2\le p\le4.$ This is based on joint work with Xing Wang and Yakun Xi.

联系人：席亚昆（yakunxi@zju.edu.cn）