Sharp pointwise convergence of Schr\"odinger operator with complex time along curves

TL;DR

This paper investigates the almost everywhere convergence of Schr"odinger operators with complex time along curves, including fractional cases, establishing sharp results up to the endpoints.

Contribution

It provides new sharp convergence results for Schr"odinger operators with complex time along curves, extending to fractional cases.

Findings

Almost everywhere convergence results established.

Results are sharp up to endpoints.

Includes fractional Schr"odinger operators.

Abstract

In this paper, we study the almost everywhere convergence results of Schr\"odinger operator with complex time along curves. We also consider the fractional cases. All results are sharp up to the endpoints.