Landis-type conjecture for the fractional Schrodinger operator (Joint with IP seminar)

In this talk, I would like to discuss Landis-type conjecture for the fractional Schrodinger
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 Schrodinger
operator, 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.