Journal article
POSITIVE MATRICES IN THE HARDY SPACE WITH PRESCRIBED BOUNDARY REPRESENTATIONS VIA THE KACZMARZ ALGORITHM
Journal d'analyse mathématique (Jerusalem), Vol.138(1), pp.209-234
07/01/2019
DOI: 10.1007/s11854-019-0026-6
Abstract
For a singular probability measure mu on the circle, we show the existence of positive matrices on the unit disc which admit a boundary representation on the unit circle with respect to mu. These positive matrices are constructed in several different ways using the Kaczmarz algorithm. Some of these positive matrices correspond to the projection of the Szego kernel on the disc to certain subspaces of the Hardy space corresponding to the normalized Cauchy transform of mu. Other positive matrices are obtained which correspond to subspaces of the Hardy space after a renormalization, and so are not projections of the Szego kernel. We show that these positive matrices are a generalization of a spectrum or Fourier frame for mu, and the existence of such a positive matrix does not require mu to be spectral.
Details
- Title: Subtitle
- POSITIVE MATRICES IN THE HARDY SPACE WITH PRESCRIBED BOUNDARY REPRESENTATIONS VIA THE KACZMARZ ALGORITHM
- Creators
- John E Herr - Iowa State UniversityPalle E. T Jorgensen - University of IowaEric S Weber - Iowa State University
- Resource Type
- Journal article
- Publication Details
- Journal d'analyse mathématique (Jerusalem), Vol.138(1), pp.209-234
- DOI
- 10.1007/s11854-019-0026-6
- ISSN
- 0021-7670
- eISSN
- 1565-8538
- Publisher
- SPRINGER
- Number of pages
- 26
- Language
- English
- Date published
- 07/01/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984241152802771
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