A. Laptev, S. Naboko, O. Safronov
Absolutely continuous spectrum of Schr\"odinger operators with slowly 
decaying and oscillating potentials
(233K, Postscript)

ABSTRACT.  The aim of this paper is to extend a class of potentials for which the 
absolutely continuous 
spectrum of the corresponding multidimensional Schr\"odinger operator is essentially 
supported by $[0,\infty)$. Our main theorem states that this property is preserved 
for slowly decaying potentials provided that there are some oscillations 
with respect to one of the variables.