Dr. Jenn-Nan Wang (National Taiwan University)

4/26/23  2:10pm

Abstract: In this talk, I would like to discuss Landis-type conjecture for the fractional Schr ̈odinger operator. This conjecture is closely related to uniqueness estimates for the strong unique continuation property and the unique continuation at infinity. These kinds of estimates are useful in understanding the local and global properties of the solution. For the classical Schrodinger operator, these estimates have been extensively studied and successfully applied to other problems. Recently, the study of the local properties of solutions to the fractional equation became possible thanks to the Caffarelli-Silvestre extension theorem. For the fractional Schr ̈odingeroperator, we are especially interested in the dependence of the estimates on the size of the potential. In the case of the half-Laplacian, we proved an almost optimal result.