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arXiv · 1803.00134

A Characterization of Boundary Representations of Positive Matrices in the Hardy Space via the Abel Product

John E. Herr·Palle E. T. Jorgensen·Eric S. Weber
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Abstract

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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John E. Herr, Palle E. T. Jorgensen, Eric S. Weber. 2018-02-28. A Characterization of Boundary Representations of Positive Matrices in the Hardy Space via the Abel Product. https://arxiv.org/abs/1803.00134

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