## Harmonic Analysis and Differential Equations Student Seminar: Semiclassical defect measures and observability estimate for Schrödinger operators with homogeneous potentials of order zero

Seminar | October 29 | 3:30-5 p.m. | 740 Evans Hall

Keita Mikami, RIKEN

Department of Mathematics

In this talk, we will consider asymptotic behavior as $x\to \infty$ of Schrödinger operators with homogeneous potentials of order zero. Localization in direction was known as a property of Schrödinger operators with homogeneous potentials of order zero or corresponding Hamiltonian flow. We will introduce this known localization in direction first. We then introduce the localization of defect measures. We then give necessary conditions for observability of Schrödinger operators with homogeneous potentials of order zero which is related to the localization result.

wangjian@berkeley.edu