 01425 A. Kiselev
 Imbedded Singular Continuous Spectrum for Schr\"odinger Operators
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Nov 18, 01

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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 ``twentyfirst 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.
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