Mini-course on “Harmonic analysis and Observability”
发文时间：2024-11-16 来源：304am永利集团
主讲人：
王明（中南大学，教授）
黄山林（华中科技大学，副教授）
时间：2024 年 11 月 16 日 9:00-12:00，14:00-17:00
2024 年 11 月 17 日 9:00-12:00，14:00-17:00
地点：永利集团，智华楼四元厅
课程内容摘要：
Part 1. Observability and uncertainty principle
1.1Observability of heat equation, thick sets and Logvinenko-Sereda uncertainty principle;
1.21-d Schrodinger equation and Logvinenko-Sereda uncertainty principle;
1.3Schrodinger equation with potentials, variable coefficient version of uncertainty principle and Ingham’s inequality.
Part 2. Logvinenko-Sereda uncertainty principle
2.1Classical version;
1.1.Fractal version with log type Hausdorff content;
1.2.Propagation of smallness for analytic functions from very small sets;
1.3.Remez inequality and Cartan lemma;
Part 3. Observability of heat equation with log content.
3.1. Generalized Lebeau-Robbiano strategy;
3.2. spectral inequality with log type Hausdorff content;
3.3. sharp gauge function.
Part 4. High dimension
4.1 Capacity and Slicing;
4.2 A transference between Hausdorff contents and capacities;
4.3 Propagation of smallness for analytic functions in higher dimension.
