Cyclicity of the shift operator and a related completeness problem in de Branges-Rovnyak spaces
Abstract
In this paper, we study the cyclic vectors of the shift operator Sb acting on de Branges-Rovnyak space H(b) associated to a non-extreme point of the closed unit ball of H∞. 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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