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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. http://resolver.caltech.edu/CaltechAUTHORS:20111027-081142498

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Abstract

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.


Item Type:Article
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http://dx.doi.org/10.1155/S107379280313084XDOIUNSPECIFIED
http://imrn.oxfordjournals.org/content/2003/36/1973.abstract?sid=1547fe1f-6a90-477e-ac87-53eb73039d50PublisherUNSPECIFIED
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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NSFDMS-0140592
Record Number:CaltechAUTHORS:20111027-081142498
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20111027-081142498
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
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:28 Oct 2011 15:01
Last Modified:28 Oct 2011 15:01

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