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

Rostyslav Kozhan

doi:10.1016/j.jat.2009.12.012

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arXiv · 0910.1975

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

Rostyslav Kozhan

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Abstract

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 and the matrix-valued result of Aptekarev-Nikishin, which handles only a finite number of mass points.

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BibTeX RIS

Rostyslav Kozhan. 2009-10-11. Szego asymptotics for matrix-valued measures with countably many bound states. https://doi.org/10.1016/j.jat.2009.12.012

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