C. Remling
The absolutely continuous spectrum of one-dimensional Schr"odinger
operators with decaying potentials
(57K, LaTeX)
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.