题目：Applications of Harmonic Analysis methods in Control Theory

时间：2024年11月25日（周一）15:00-17:00

地点：数学与统计楼213会议室

报告人：黄山林 副教授 华中科技大学

摘要：

In this talk, we'll explore interesting and natural applications of harmonic analysis tools in mathematical control theory. The classic Lebeau-Robiano spectral inequality is crucial for the observability of the heat equation. We first review recent results linking the spectral inequality to the uncertainty principle in harmonic analysis, then we discuss extending similar results to fractal sets in unbounded domains. Finally, we'll discuss the role of the spectral inequality (for high frequencies) in the Schrödinger equation with a confining potential, highlighting how spectral gaps influence the observation region's geometry through harmonic and anharmonic oscillators.

报告人简介：

黄山林，华中科技大学数学与统计学院副教授，研究方向为调和分析及其应用，目前主要从事不确定原理、薛定谔方程解的定量唯一性及有关控制问题的研究，相关研究成果发表于AJM、CMP、Adv. Math、JFA、JDE等国际数学权威学术期刊。