Sharp convergence for sequences of Schrödinger means and related generalizations

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.