Published 2003
| public
Journal Article
The Golinskii-Ibragimov Method and a Theorem of Damanik and Killip
- Creators
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Simon, Barry
Chicago
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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.
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.Additional details
- Eprint ID
- 27472
- Resolver ID
- CaltechAUTHORS:20111027-081142498
- NSF
- DMS-0140592
- Created
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2011-10-28Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field