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Szegő asymptotics for matrix-valued measures with countably many bound states

Kozhan, Rostyslav (2010) Szegő asymptotics for matrix-valued measures with countably many bound states. Journal of Approximation Theory, 162 (6). pp. 1211-1224. ISSN 0021-9045.

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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.

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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.
Subject Keywords:Szegő asymptotics; Orthogonal polynomials; Matrix-valued measures
Issue or Number:6
Record Number:CaltechAUTHORS:20101012-084432249
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20391
Deposited By: Tony Diaz
Deposited On:25 Oct 2010 17:22
Last Modified:03 Oct 2019 02:09

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