A. Kiselev
Imbedded Singular Continuous Spectrum for Schr\"odinger Operators
(406K, Postscript)

ABSTRACT.  We construct examples of potentials $V(x)$ satisfying 
$|V(x)| \leq \frac{h(x)}{1+x},$ 
where the function $h(x)$ is growing arbitrarily slowly, such that 
the corresponding Schr\"odinger 
operator has imbedded singular continuous spectrum. This solves 
one of the fifteen ``twenty-first century" 
problems for Schr\"odinger operators posed 
by Barry Simon. The construction also provides the 
first example of a Schr\"odinger operator for 
which M\"oller wave operators exist but are not asymptotically 
complete due to the presence of singular continuous spectrum.