Jost asymptotics for matrix orthogonal polynomials on the real line

Rostyslav Kozhan

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arXiv · 1104.0460

Jost asymptotics for matrix orthogonal polynomials on the real line

Rostyslav Kozhan

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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.

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BibTeX RIS

Rostyslav Kozhan. 2011-04-04. Jost asymptotics for matrix orthogonal polynomials on the real line. https://arxiv.org/abs/1104.0460

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