In 1971, Golinskii and Ibragimov proved that if the Verblunsky coefficients, {αn}n=0, of a measure dμ on ∂D obey n=0n|αn|2<, then the singular part, dμs, of dμ vanishes. We show how to use extensions of their ideas to discuss various cases where n=0Nn|αn|2 diverges logarithmically. As an application, we provide an alternative to a part of the proof of a recent theorem of Damanik and Killip.

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