# A characterization of boundary representations of positive matrices in the Hardy space via the Abel product

@article{Herr2019ACO,
title={A characterization of boundary representations of positive matrices in the Hardy space via the Abel product},
author={John E. Herr and Palle E. T. Jorgensen and Eric S. Weber},
journal={Linear Algebra and its Applications},
year={2019}
}
• Published 28 February 2018
• Mathematics
• Linear Algebra and its Applications
Spectral measures give rise to a natural harmonic analysis on the unit disc via a boundary representation of a positive matrix arising from a spectrum of the measure. We consider in this paper the reverse: for a positive matrix in the Hardy space of the unit disc we consider which measures, if any, yield a boundary representation of the positive matrix. We prove a characterization of those representing measures via a matrix identity by introducing a new operator product called the Abel Product.
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