Contractive upper triangular matrices with prescribed diagonals and superdiagonals
Functional Analysis
2025-06-24 v1
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.
Keywords
Cite
@article{arxiv.2506.15444,
title = {Contractive upper triangular matrices with prescribed diagonals and superdiagonals},
author = {Axel Renard},
journal= {arXiv preprint arXiv:2506.15444},
year = {2025}
}