Published June 2010
| public
Journal Article
Szegő asymptotics for matrix-valued measures with countably many bound states
- Creators
- Kozhan, Rostyslav
Abstract
Let μ be a matrix-valued measure with the essential spectrum a single interval and countably many point masses outside of it. Under the assumption that the absolutely continuous part of μ satisfies Szegő's condition and the point masses satisfy a Blaschke-type condition, we obtain the asymptotic behavior of the orthonormal polynomials on and off the support of the measure. The result generalizes the scalar analogue of Peherstorfer–Yuditskii (2001) [12] and the matrix-valued result of Aptekarev–Nikishin (1983) [1], which handles only a finite number of mass points.
Additional Information
© 2010 Published by Elsevier Inc. Received 21 August 2009; revised 23 December 2009; accepted 31 December 2009. Communicated by Serguei Denissov. Available online 11 January 2010. The author would like to thank Barry Simon for helpful discussions.Additional details
- Eprint ID
- 20391
- Resolver ID
- CaltechAUTHORS:20101012-084432249
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2010-10-25Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field