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Let $\mu$ be a matrix-valued measure with the essential spectrum a singleinterval and countably many point masses outside of it. Under the assumptionthat the absolutely continuous part of $\mu$ satisfies Szego's condition andthe point masses satisfy a Blaschke-type condition, we obtain the asymptoticbehavior of the orthonormal polynomials on and off the support of the measure.  The result generalizes the scalar analogue of Peherstorfer-Yuditskii and thematrix-valued result of Aptekarev-Nikishin, which handles only a finite numberof mass points.

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