Improved resolvent bounds for radial potentials. II

Abstract

We prove semiclassical resolvent estimates for the Schr{\"o}dinger operator in R d , d $\ge$ 3, with real-valued radial potentials V $\in$ L $\infty$ (R d). We show that if V (x) = O x --$\delta$ with $\delta$ > 4, then the resolvent bound is of the form exp Ch -- $\delta$ $\delta$--1 log(h --1) 1 $\delta$--1 with some constant C > 0. If V (x) = O e -- C x $\alpha$ with C, $\alpha$ > 0, we get better resolvent bounds of the form exp Ch --1 log(h --1