Alexei Rybkin
On the absolutely continuous and negative discrete spectra of Schrodinger operators on the line with locally integrable globally square summable potentials 
(31K, AMS-TeX)

ABSTRACT.  For one-dimensional Schrodinger operators with potentials $q$ subject to 
\begin{equation*} 
\sum_{n=-\infty }^{\infty }\left( \int_{n}^{n+1}\left\vert q\left( x\right) 
\right\vert dx\right) ^{2}<\infty 
\end{equation*} 
we prove that the absolutely continuous spectrum is $[0,\infty )$, extending 
the 1999 result due to Dieft-Killip. As a by-product we show that under the 
same condition the sequence of the negative eigenvalues is $3/2-$summable 
improving the relevant result by Lieb-Thirring.