Abstract

In 1971, Golinskii and Ibragimov proved that if the Verblunsky coefficients, ${αn}n=0∞$, of a measure dμ on ∂D obey $∑n=0∞n|αn|2<∞$, 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.