Abstract
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∞ and compactly supported. The weighted resolvent norm grows no faster than exp(Ch−1), while an exterior weighted norm grows ∼h−1. We introduce a new method based on the Mellin transform to handle the two-dimensional case.
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