北航学术报告

--- 分析、偏微分方程与动力系统讨论班(2025秋季第3讲)

Logvinenko-Sereda sets and Carleson measures on compact manifolds

王兴（湖南大学）

时间：2025年09月17日（周三）上午9:00-10:00

地点：学院路老主楼105

摘要: Marzo and Ortega-Cerd`a gave geometric characterizations for L^p-Logvinenko-Sereda sets on the standard sphere. Later, Ortega-Cerd`a and Pridhnani further investigated L^2-Logvinenko-Sereda sets and L^2-Carleson measures on compact manifolds without boundary. In this paper, we  characterize L^p-Logvinenko-Sereda sets and L^p-Carleson measures on compact manifolds with or without boundary for all 1<p<\infty.   Furthermore, we investigate Logvinenko-Sereda sets and Carleson measures for eigenfunctions on compact manifolds without boundary, and we completely characterize them on the standard sphere for p > \frac{2m}{m-1}. For the range p < \frac{2m}{m-1}, we conjecture that L^p-Logvinenko-Sereda sets on the standard sphere are characterized by the tubular geometric control condition and we provide some evidence. These results provide new progress on an open problem raised  by Ortega-Cerd`a and Pridhnani.  

报告人简介: 王兴，湖南大学数学学院副教授。美国约翰霍普金斯大学博士学位，师从Christopher Sogge 教授.主要研究方向是流形上的调和分析及算子谱的渐近性质，Advances in Mathematics, Transactions of the American Mathematical Society, Canadian Journal of Mathematics, Proceedings of the American Mathematical Society，Mathematical Research Letters 等学术期刊上发表多篇学术论文。

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