Regularity of Solution of the Schr\"odinger Equation on Symmetric Space

In this article, we investigate the behavior of solutions $u(x,t)$ to the fractional Schr\"odinger 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 Sj\"olin's results in this setting.