Jost Asymptotics for Matrix Orthogonal Polynomials on the Real Line |
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Authors: | Rostyslav Kozhan |
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Institution: | 1. Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, CA, 90095, USA
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Abstract: | We obtain matrix-valued Jost asymptotics for block Jacobi matrices under an L 1-type condition on Jacobi coefficients, 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 and Simon (Int. Math. Res. Not. 32:19396, 2006). The above results allow us to fully characterize the Weyl?CTitchmarsh m-functions of Jacobi matrices with exponentially converging parameters. |
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