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.

The main purpose of the paper is to give a characterization all compactly supported dual windows Gabor frame. As an application, we consider iterative procedure for approximation canonical window via on every step. In particular, allows have from certain modulation spaces or Schwartz space.