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arXiv · 2403.04335

Cyclicity of the shift operator and a related completeness problem in de Branges-Rovnyak spaces

Emmanuel Fricain·Romain Lebreton
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Abstract

In this paper, we study the cyclic vectors of the shift operator $S_b$ acting on de Branges-Rovnyak space $\mathcal H(b)$ associated to a non-extreme point of the closed unit ball of $H^\infty$. We highlight an interesting link with a completeness problem that we study using the Cauchy transform. This enables us to obtain some nice consequences on cyclicity.

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Emmanuel Fricain, Romain Lebreton. 2024-03-07. Cyclicity of the shift operator and a related completeness problem in de Branges-Rovnyak spaces. https://arxiv.org/abs/2403.04335

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