Sharp convergence rate of Schr\"odinger operator along curves

TL;DR

This paper investigates the convergence rate of Schrödinger operators along curves, providing sharp results up to the endpoints, which advances understanding of their behavior in harmonic analysis.

Contribution

It establishes the sharp convergence rates of Schrödinger operators along curves, filling gaps in the existing theory with endpoint sharpness.

Findings

Convergence rates are sharp up to endpoints.

Results apply to functions in Sobolev spaces.

Enhanced understanding of Schrödinger operators along curves.

Abstract

We analyze convergence rate of Schr\"odinger operator along curves $U_{\gamma}f(x,t)$, where $f \in H^{s}\left(\mathbb{R}^{d}\right)$. All results are sharp up to the endpoints.