Completely hyperexpansive operators with finite rank defect operator and de Branges-Rovnyak spaces

2024/05/23 by Joshi, Saee A., Sholapurkar, Vinayak M.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2405.14694

Abstract

The process of identifying a Dirichlet-type space D(μ) for a positive, Borel measure μ, supported on the unit circle \mathbb T, with a de Branges-Rovnyak space was initiated by Sarason. A characterization of the symbol for a de Branges-Rovnyak spaces for which the shift operator is a 2-isometry, was provided in an article by Kellay and Zarrabi. In this paper, capitalizing on the Aleman's model for the cyclic, analytic, completely hyperexpansive operators, we provide a characterization of cyclic, analytic, completely hyperexpansive operator with finite rank defect operator in terms of the symbol for a de Branges-Rovnyak space.

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