Sharp convergence for sequences of Schrödinger means and related generalizations
Sharp convergence for sequences of Schrödinger means and related generalizations
For decreasing sequences $\{t_{n}\}_{n=1}^{\infty }$ converging to zero and initial data $f\in H^s(\mathbb {R}^N)$ , $N\geq 2$ , we consider the almost everywhere convergence problem for sequences of Schrödinger means ${\rm e}^{it_{n}\Delta }f$ , which was proposed by Sjölin, and was open until recently. In this paper, we prove that …