3 research outputs found
Szego asymptotics for matrix-valued measures with countably many bound states
Let 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 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
Jost asymptotics for matrix orthogonal polynomials on the real line
We obtain matrix-valued Jost asymptotics for block Jacobi matrices under an
L1-type condition on Jacobi parameters, and give a necessary and sufficient
condition for an analytic matrix-valued function to be the Jost function of a
block Jacobi matrix with exponentially converging parameters. This establishes
the matrix-valued analogue of Damanik-Simon-II paper [6]. The above results
allow us to fully characterize the matrix-valued Weyl-Titchmarsh m-functions of
block Jacobi matrices with exponentially converging parameters