 97375 C. Remling
 The absolutely continuous spectrum of onedimensional Schr"odinger
operators with decaying potentials
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Jun 26, 97

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Abstract. We investigate onedimensional Schr"odinger operators with
asymptotically small potentials. It will follow from our
results that if V(x)=O(x^{c}) with c>1/2, then (0,\infty)
is an essential support of the absolutely continuous part
of the spectral measure.
We also prove that if C=limsup_{x\to\infty} xV(x)<\infty,
then the spectrum is purely absolutely continuous on
(0,\infty).
These results are optimal.
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