 99189 Zhongwei Shen
 On Absolute Continuity of the Periodic Schrodinger Operators
(58K, AMSTeX)
May 20, 99

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Abstract. This paper concerns the Schrodinger operator $\Delta +V$ in
$R^d$, $d\ge 3$, with periodic potential $V$. Under the assumption
$V\in L^{d/2}_{loc} (R^d)$, it is shown that the spectrum of $\Delta +V$
is purely absolutely continuous. The condition on the potential $V$
is optimal in the context of $L^p$ spaces. The proof relies on certain
uniform Sobolev inequalities on the dtorus. We also establish the
absolute continuity of $\Delta +V$ with certain periodic potential
$V$ in the weakL^{d/2} space.
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