Contractive upper triangular matrices with prescribed diagonals and superdiagonals
arXiv:2506.15444 · doi:10.1016/j.laa.2025.06.012
Abstract
A characterization of the matrix representation of the compressed shift acting on a finite-dimensional model space endowed with the Takenaka-Malmquist-Walsh basis, among all upper triangular matrices, is proved. For a fixed dimension, this matrix is the unique matrix with spectral norm no greater than one and with a prescribed diagonal and superdiagonal. We also discuss an extension to the setting of infinite matrices.