Uniform resolvent estimates, unique continuation and control

讲座时间 Datetime: 2021年9月17日 ，星期五，19:00-20:30

地点 Venue: 腾讯会议，451 563 626

报告人 Speaker:  黄山林 副教授

单位 Affiliation: 华中科技大学

报告摘要 Abstract:

In this talk, we first recall a classical L^p (uniform) resolvent estimate established by Kenig, Ruiz and Sogge in the 1980s, which is closely related to the unique continuation problems of Schrodinger operators with singular potentials. Then we turn to another type of L^2 (uniform) resolvent estimate (a.k.a Hautus-type test), which is equivalent to the exact controllability for the linear Schrodinger equation. Based on this approach, we give some recent results concerning the observability of the 1-d Schrodinger equation with potentials x^{2m}, m=0,1,2,...