Cyclicity of the Shift Operator and a Related Completeness Problem in de Branges–Rovnyak Spaces

Emmanuel Fricain () and Romain Lebreton ()
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Emmanuel Fricain: CNRS, UMR 8524 – Laboratoire Paul Painlevé, Univ. Lille
Romain Lebreton: CNRS, UMR 8524 – Laboratoire Paul Painlevé, Univ. Lille

Chapter 77 in Operator Theory, 2026, pp 2389-2410 from Springer

Abstract: Abstract In this chapter, we study the cyclic vectors of the shift operator S b $$S_b$$ acting on de Branges–Rovnyak space ℋ ( b ) $$\mathcal H(b)$$ associated with a non-extreme point of the closed unit ball of H ∞ $$H^\infty $$ . 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.

Keywords: Cyclicity; de Branges–Rovnyak spaces; Shift operator; Cauchy transform; 30J05; 30H10; 46E22 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16356-1_108

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