  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.
