 9987 C. Remling
 Schr\"odinger operators with decaying potentials:
some counterexamples
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Mar 29, 99

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Abstract. Consider the onedimensional Schr\"odinger operator
$H=d^2/dx^2 +V(x)$ on $L_2(0,\infty)$. It's known that
if $V(x) \le C(1+x)^{\alpha}$ with $1/2 < \alpha \le 1$,
then $H$ has absolutely continuous spectrum on $[0,\infty)$,
with possibly also some embedded singular spectrum there.
Here, we construct examples which show that recently
obtained results on the singular spectrum are in fact
optimal.
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