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. https://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.
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| 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 | |||||||||
| DOI: | 10.1155/S107379280313084X | |||||||||
| Record Number: | CaltechAUTHORS:20111027-081142498 | |||||||||
| Persistent URL: | https://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: | 09 Nov 2021 16:49 |
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