Sharp pointwise convergence of Schrödinger mean with complex time in higher dimensions

Abstract

In this paper, we establish the almost everywhere convergence of solutions to the Schrödinger operator with complex time $P_{\hat{I}}^{3}f(x,t)$ in higher dimensions, under the assumption that the initial data $f$ belongs to the Sobolev space $H^s({\mathbb{R}}^d)$.

14 pages