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In this chapter, we study the cyclic vectors of the shift operator Sb acting on de Branges–Rovnyak space \(\mathcal H(b)\) associated with 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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Cyclicity of the Shift Operator and a Related Completeness Problem in de Branges–Rovnyak Spaces

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  • 发表日期：

    2025年

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  • Emmanuel Fricain,
  • Romain Lebreton

摘要

In this chapter, we study the cyclic vectors of the shift operator Sb acting on de Branges–Rovnyak space \(\mathcal H(b)\) associated with 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.