The first Szegő limit theorem on multi-dimensional torus

Kunyu Guo, Dilong Li, Qi Zhou

In this paper, we consider the first Szegő limit theorems on $d$-torus ${\mathbb{T}}^d$ for $1\le d\le +\infty$. It is shown that for any Følner sequence $\{{\sigma }_N\}$ of $\mathbb{Z}^d…