Verblunsky-type coefficients for Dirac and canonical systems generated by Toeplitz and Hankel matrices, respectively
Spectral Theory
2020-07-03 v1 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.1711.03064,
title = {Verblunsky-type coefficients for Dirac and canonical systems generated by Toeplitz and Hankel matrices, respectively},
author = {Alexander Sakhnovich},
journal= {arXiv preprint arXiv:1711.03064},
year = {2020}
}