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

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

John E Herr, Palle E T Jorgensen and Eric S Weber
Frames and harmonic analysis: AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16–17, 2016, North Dakota State University, Fargo, North Dakota, pp.255-270
Contemporary mathematics, 706, American Mathematical Society
2018
DOI: 10.1090/conm/706

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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 introduce a potential characterization of those measures via a matrix identity and show that the characterization holds in several important special cases.

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