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Resonance-free regions for diffractive trapping by conormal potentials
We consider the Schr\"odinger operator $$ P=h^2\Delta_g +V $$ on $\Bbb{R}^n$ equipped with a metric $g$ that is Euclidean outside a compact set. The real-valued potential $V$ is assumed to be compactly supported and smooth except at {\it conormal singularities} of order $-1-\alpha$ along a compact hypersurface $Y$. For $\alpha>2$ …