99-87 C. Remling
Schr\"odinger operators with decaying potentials: some counterexamples (84K, LaTeX 2e) Mar 29, 99
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Abstract. Consider the one-dimensional 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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