Resonances as Viscosity Limits for Exterior Dilation Analytic Potentials

Abstract

For exterior dilation analytic potential, $V$, we use the method of complex scaling to show that the resonances of $-\Delta +V$, in a conic neighbourhood of the real axis, are limits of eigenvalues of $-\Delta +V-i\epsilon x^2$ as $\epsilon \to 0+$, if $V$ can be analytically extended from ${\mathbb{R}}^n$ to a truncated cone in ${\mathbb{C}}^n$.