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The Golinskii-Ibragimov Method and a Theorem of Damanik and Killip

Simon, Barry (2003) The Golinskii-Ibragimov Method and a Theorem of Damanik and Killip. International Mathematics Research Notices, 2003 (36). pp. 1973-1986. ISSN 1073-7928. doi:10.1155/S107379280313084X.

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In 1971, Golinskii and Ibragimov proved that if the Verblunsky coefficients, {α_n}_n^∞ = 0, of a measure dμ on ∂D obey ∑_(n=0)^∞^n│α_n│^2 < ∞, then the singular part, dμs, of dμ vanishes. We show how to use extensions of their ideas to discuss various cases where ∑_(n=0)^N^n│α_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.

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Simon, Barry0000-0003-2561-8539
Additional Information:© 2003 Hindawi Publishing Corporation. Received March 13, 2003. Accepted June 8, 2003. Communicated by Percy Deift. This work was supported in part by the National Science Foundation (NSF) grant DMS-0140592. It is a pleasure to thank David Damanik and Rowan Killip for telling me about their work and for useful discussions.
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Issue or Number:36
Record Number:CaltechAUTHORS:20111027-081142498
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Official Citation:Barry Simon The Golinskii-Ibragimov method and a theorem of Damanik and Killip Int Math Res Notices (2003) Vol. 2003 1973-1986 doi:10.1155/S107379280313084X
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27472
Deposited By: Ruth Sustaita
Deposited On:28 Oct 2011 15:01
Last Modified:09 Nov 2021 16:49

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