Analysis/PDE Seminar: Rough control for Schrödinger operators on 2-tori.
Seminar | November 19 | 4:10-5 p.m. | 740 Evans Hall
Maciej Zworski, UC Berkeley
I will explain how the results of Bourgain, Burq and the speaker '13 can be used to obtain control and observability by rough functions and sets on 2-tori. We show that for the time dependent Schrödinger equation, any set of positive measure can be used for observability and controllability.
For non-empty open sets this follows from the results of Haraux '89 and Jaffard '90, while for sufficiently long times and rational tori this can be deduced from the results of Jakobson '97.