On the asymptotic behavior of the spectral characteristics of exterior problems for the Schrödinger operator

The Green's function $G(x,y;\lambda)$, $x,y\in\Omega$, $\lambda>0$, of the Schrödinger equation $-\Delta_xG+v(x)G-\lambda G=\delta(x-y)$ satisfying a radiation condition at infinity is considered in the exterior $\Omega$ of a convex smooth closed hypersurface $\Gamma$ in $R^m$. The potential is assumed to be a smooth function with compact support. Asymptotic formulas for $\lambda\to\infty$that are uniform in $x$ and $y$ are obtained.
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