Jost asymptotics for matrix orthogonal polynomials on the real line

Details Jost asymptotics for matrix orthogonal polynomials on the real line Jost asymptotics for matrix orthogonal polynomials on the real line

2011-04-04

arxiv.org/abs/1104.0460v2

Mathematics

Analysis of PDEs

Scientific paper

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.

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