Semiclassical resolvent estimates for short-range $L^\infty$ potentials

Abstract

We prove semiclassical resolvent estimates for real-valued potentials $V\in L^{\infty }\left({ℝ}^n\right)$, $n\ge 3$, satisfying $V\left(x\right)=\mathcal{O}\left({\langle x\rangle }^{-\delta }\right)$ with $\delta >3$.