02-11 S.A.Denisov

On the continuous analog of the Rakhmanov's theorem for orthogonal polynomials (preliminary version). (35K, LATEX) Jan 7, 02

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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.

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