Research Seminars

Abstract

For decreasing sequences $\{t_{n}\}_{n=1}^{\infty}$ converging to zero, we obtain the almost everywhere  convergence results for sequences of Schr\"{o}dinger means $e^{it_{n}\Delta}f$, where $f \in H^{s}(\mathbb{R}^{N}), N\geq 2$. The convergence results are sharp up to the endpoints, and the method can also be applied  to get the convergence results for the fractional Schr\"{o}dinger means  and nonelliptic Schr\"{o}dinger means. This is a joint work with Dr. Huijv Wang and Prof. Dunyan Yan.

In this talk, I will introduce the background of the above convergence problem, and show the main results we have obtained so far.