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Cyclicity of the shift operator and a related completeness problem in de Branges-Rovnyak spaces (2403.04335v1)
Published 7 Mar 2024 in math.CV and math.FA
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.