Oleg Safronov
The rate of accumulation of negative eigenvalues to zero and the absolutely continuous spectrum
(419K, pdf)

ABSTRACT.  For a bounded real-valued function $V$ on ${\Bbb R}^d$, we consider two Schr\"odinger operators $H_+=-\Delta+V$ and $H_-=-\Delta-V$. 
We prove that if the negative spectra $H_+$ and $H_-$ are discrete and the negative eigenvalues of $H_+$ and $H_-$ tend to zero 
sufficiently fast, then 
 the absolutely continuous spectra cover the positive half-line $[0,\infty)$.