- 03-364 Alexei Rybkin
- On the absolutely continuous and negative discrete spectra of Schrodinger operators on the line with locally integrable globally square summable potentials
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Aug 10, 03
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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.
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