Semiclassical resolvent bounds for weakly decaying potentials

22 Mar 2020 Galkowski Jeffrey Shapiro Jacob

In this note, we prove weighted resolvent estimates for the semiclassical Schr\"odinger operator $-h^2 \Delta + V(x) : L^2(\mathbb{R}^n) \to L^2(\mathbb{R}^n)$, $n \neq 2$. The potential $V$ is real-valued, and assumed to either decay at infinity or to obey a radial $\alpha$-H\"older continuity condition, $0\leq \alpha \leq 1$, with sufficient decay of the local radial $C^\alpha$ norm toward infinity... (read more)

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