A matrix characterization of boundary representations of positive matrices in the Hardy space

@article{Herr2017AMC,
  title={A matrix characterization of boundary representations of positive matrices in the Hardy space},
  author={John E. Herr and Palle E. T. Jorgensen and Eric S. Weber},
  journal={arXiv: Functional Analysis},
  year={2017}
}
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 introduce a potential characterization of those measures via a matrix identity and show that the characterization holds in several important… 
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