Oleg Safronov
Multi-dimensional Schr\"odinger operators with no negative 
spectrum
(157K, Postscript)

ABSTRACT.  We consider multi-dimensional Schr\"odinger operators $-\Delta \pm V$ 
with a bounded real potential $V$. 
We prove that if both $-\Delta + V$ and $-\Delta - V$ have no spectrum inside $(-\infty,0)$, then they must have absolutely continuous spectrum essentially supported by the positive real line.