Published 2013
| Submitted
Journal Article
Open
Orthogonal Polynomials on the Unit Circle with Verblunsky Coefficients defined by the Skew-Shift
- Creators
- Krüger, Helge
Abstract
I give an example of a family of orthogonal polynomials on the unit circle with Verblunsky coefficients given by the skew-shift for which the associated measures are supported on the entire unit circle and almost every Aleksandrov measure is pure point. Furthermore, I show in the case of the two-dimensional skew-shift that the zeros of para-orthogonal polynomials obey the same statistics as an appropriate irrational rotation. The proof is based on an analysis of the associated CMV matrices.
Additional Information
© The Author(s) 2012. Published by Oxford University Press. Received January 13, 2012; Revised June 13, 2012; Accepted June 19, 2012. Communicated by Prof. Percy Deift. Advance Access Publication July 18, 2012. The key realization that Proposition 5.1 and Lemma 5.2 hold came to me during discussions with Darren Ong. Furthermore, I am thankful to Maxim Zinchenko for correspondence, which clarified issues related to (3.27). Lastly, I am thankful to the referees whose comments helped improve the presentation. This research was supported by a fellowship of the Simons foundation (to H.K.).Attached Files
Submitted - 1111.4019v1.pdf
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Additional details
- Eprint ID
- 42512
- DOI
- 10.1093/imrn/rns173
- Resolver ID
- CaltechAUTHORS:20131118-081812939
- Simons Foundation
- Created
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2013-11-18Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field