97-375 C. Remling

The absolutely continuous spectrum of one-dimensional Schr"odinger operators with decaying potentials (57K, LaTeX) Jun 26, 97

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Abstract. We investigate one-dimensional 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} x|V(x)|<\infty, then the spectrum is purely absolutely continuous on (0,\infty). These results are optimal.

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