Uniform Resolvent Estimates for the Discrete Schrödinger Operator in Higher Dimensions

Yuda Chen

Let $H_0$ be the standard discrete Laplacian on ${\mathbb{Z}}^d$, $d\ge 4$, let $R_0(z)=(H_0-z{)}^{-1}$, and let $p^{\prime }$ denote the Hölder conjugate of $p$, with $p^{\prime }=\infty$ when $p=1$. We…