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

作者：Kozhan Rostyslav^*

来源：Journal of Approximation Theory, 2010, 162(6): 1211-1224.

DOI：10.1016/j.jat.2009.12.012

• Szego asymptotics
• Orthogonal polynomials
• Matrix-valued measures

Let mu 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 mu satisfies Szego'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. Published by Elsevier Inc.

• 出版日期2010-6