  We prove a dispersive estimate for the evolution of Schroedinger operators $H
= -\Delta + V(x)$ in ${\mathbb R}^3$. The potential is allowed to be a
complex-valued function belonging to $L^p(\R^3)\cap L^q(\R^3)$, $p < \frac32 <
q$, so that $H$ need not be self-adjoint or even symmetric. Some additional
spectral conditions are imposed, namely that no resonances of $H$ exist
anywhere within the interval $[0,\infty)$ and that eigenfunctions at zero
(including generalized eigenfunctions) decay rapidly enough to be integrable.

Analysis of PDEs