Brian Choi

Boston University

Talk Title: Pointwise Convergence of Schroedinger Operator to the Identity

Abstract: We consider Carleson’s problem regarding small time almost everywhere convergence to the initial data for the Schroedinger equation, both linear and nonlinear. We show that the (sharp) result proved by Dahlberg and Kenig for initial conditions in Sobolev spaces of order $s\geq \frac{1}{4}$ still holds when one considers the Schroedinger equation with a certain class of potentials. As for $s<\frac{1}{4}$, we show that there exists a large class of functions in the corresponding Sobolev space that fails to exhibit pointwise convergence to initial data by studying the integral kernel of Schroedinger operator provided that the potential is sufficiently regular.