New "Verblunsky-type" coefficients of block Toeplitz and Hankel matrices and of corresponding Dirac and canonical systems

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.

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