Barry Simon
The Golinskii-Ibragimov Method and a Theorem of Damanik and Killip
(33K, AMS-LaTeX)
ABSTRACT. In 1971, Golinskii and Ibragimov proved that if the Verblunsky coefficients,
$\{\alpha_n\}_{n=0}^\infty$, of a measure $d\mu$ on $\partial\bbD$ obey $\sum_{n=0}^\infty n
\abs{\alpha_n}^2 <\infty$, then the singular part, $d\mu_\s$, of $d\mu$ vanishes. We show how
to use extensions of their ideas to discuss various cases where $\sum_{n=0}^N n \abs{\alpha_n}^2$
diverges logarithmically. As an application, we provide an alternative to a part of the proof of
a recent theorem of Damanik and Killip.