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arXiv · 2405.14694

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

Saee A. Joshi·Vinayak M. Sholapurkar
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Abstract

The process of identifying a Dirichlet-type space $D(\mu)$ for a positive, Borel measure $\mu$, 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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Saee A. Joshi, Vinayak M. Sholapurkar. 2024-05-23. Completely hyperexpansive operators with finite rank defect operator and de Branges-Rovnyak spaces. https://arxiv.org/abs/2405.14694

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