Abstract

We obtain matrix-valued Jost asymptotics for block Jacobi matrices under an L1-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).

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