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Published June 2010 | public
Journal Article

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

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

Created:
August 22, 2023
Modified:
October 20, 2023