S.A.Denisov
On the continuous analog of the Rakhmanov's theorem for 
orthogonal polynomials (preliminary version).
(35K, LATEX)

ABSTRACT.  We obtain the continuous analogs of Rakhmanov's theorem for polynomials orthogonal on the unit circle. 
Sturm-Liouville operators and Krein systems are considered. Under some conditions on the potential 
$q$ of the S.L. operator, we prove that if a.c. component of the spectrum fills the whole half-line, 
then $q$ decays at infinity.