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 $\mathbb{C}^n$.