Verblunsky-type coefficients for Dirac and canonical systems generated by Toeplitz and Hankel matrices, respectively

Abstract

We introduce Verblunsky-type coefficients of Toeplitz and Hankel matrices, which correspond to the discrete Dirac and canonical systems generated by Toeplitz and Hankel matrices, respectively. We prove one to one correspondences between positive-definite Toeplitz (Hankel) matrices and their Verblunsky-type coefficients as analogs of the well-known Verblunsky's theorem. Several interconnections with the spectral theory are described as well.

References in corpus (1)

• General-type discrete self-adjoint Dirac systems: explicit solutions of direct and inverse problems, asymptotics of Verblunsky-type coefficients and stability of solving inverse problem

Cited by in corpus (6)

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• Discrete Dirac systems on the semiaxis: rational reflection coefficients and Weyl functions
• General-type discrete self-adjoint Dirac systems: explicit solutions of direct and inverse problems, asymptotics of Verblunsky-type coefficients and stability of solving inverse problem
• Arov--Krein entropy functionals and indefinite interpolation problems
• On the solution of the inverse problem for a class of canonical systems corresponding to matrix string equations