Semiclassical resolvent bounds for compactly supported radial potentials

We employ separation of variables to prove weighted resolvent estimates for the semiclassical Schrödinger operator −h2Δ+V(|x|)−E in dimension n≥2, where h,E>0, and V:[0,∞)→R is L∞ compactly supported. The norm grows no faster than exp⁡(Ch−1), while an exterior ∼h−1. introduce a new method based on Mellin transform handle two-dimensional case.