The derivative of the fractional discrete Laplacian is an exotic Riesz potential

Bo Li, Qingze Lin, Huoxiong Wu

Let ${\Delta }_N$ be the multidimensional discrete Laplacian on ${\mathbb{Z}}^N$ ($N\ge 1$). In this note, we prove that, when $N=1$, the right hand derivative of $(-{\Delta }_1{)}^s$ at $0$ is an ex…