Book chapter
A matrix characterization of boundary representations of positive matrices in the Hardy space
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
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.
Details
- Title: Subtitle
- A matrix characterization of boundary representations of positive matrices in the Hardy space
- Creators
- John E HerrPalle E T Jorgensen - University of Iowa, MathematicsEric S Weber
- Resource Type
- Book chapter
- Publication Details
- 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
- Series
- Contemporary mathematics; 706
- DOI
- 10.1090/conm/706
- Publisher
- American Mathematical Society; Providence, Rhode Island
- Language
- English
- Date published
- 2018
- Academic Unit
- Mathematics
- Record Identifier
- 9983986089902771
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