Jost asymptotics for matrix orthogonal polynomials on the real line

Abstract

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.

arXiv commentThis is the updated version of the paper in Constr. Approx. 36 (2012), no. 2, pp.267-309 that corrects an error in Lemma 2.19 and a few other inaccuracies