Improved resolvent bounds for radial potentials. II

2022/03/08 by Vodev, Georgi · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.03941

Abstract

We prove semiclassical resolvent estimates for the Schrödinger operator in R d , d ≥ 3, with real-valued radial potentials V ∈ L ∞ (R d). We show that if V (x) = O x --δ with δ > 4, then the resolvent bound is of the form exp Ch -- δ δ--1 log(h --1) 1 δ--1 with some constant C > 0. If V (x) = O e -- C x α with C, α > 0, we get better resolvent bounds of the form exp Ch --1 log(h --1

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