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

2017/05/09 by John E. Herr, Herr, John E., Palle E. T. Jørgensen +3
Computer Science · Mathematics · #28A25 (Secondary) #30B30 (Primary) #42B05 #46E22 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1705.04198

openalex publication_date 2017/05/09 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Spectral measures give rise to a natural harmonic analysis on the unit disc\nvia a boundary representation of a positive matrix arising from a spectrum of\nthe measure. We consider in this paper the reverse: for a positive matrix in\nthe Hardy space of the unit disc we consider which measures, if any, yield a\nboundary representation of the positive matrix. We introduce a potential\ncharacterization of those measures via a matrix identity and show that the\ncharacterization holds in several important special cases.\n

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