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arXiv · 2506.15444

Contractive upper triangular matrices with prescribed diagonals and superdiagonals

Axel Renard
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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.

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Axel Renard. 2025-06-18. Contractive upper triangular matrices with prescribed diagonals and superdiagonals. https://doi.org/10.1016/j.laa.2025.06.012

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