Regularity of Solution of the Schrödinger Equation on Symmetric Space

Abstract

In this article, we investigate the behavior of solutions \( u(x,t) \) to the fractional Schrödinger equation on rank symmetric spaces of non-compact type. We proved that as time \( t \) approaches $0$, then $u(x,t)$ converges pointwise almost everywhere to the initial radial data \( f \), provided that \( f \in H^s(\mathbb{X}) \) with \( s > \frac{1}{2} \). This result extends Sjölin's results in this setting.

11 pages