Königs maps and commutants of composition operators on the Hardy-Hilbert space of Dirichlet series

2024/06/28 by Frédéric Bayart, Xingxing Yao, Bayart, Frédéric +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2406.19737

openalex created_date 2024/06/28 · openalex publication_date 2024/06/28 · openalex updated_date 2026/07/28

Abstract

Let φ be a holomorphic map which is a symbol of a bounded composition operator C_φ acting on the Hardy-Hilbert space of Dirichlet series. We find a Königs map for φ. We then deduce several applications on C_φ (e.g. on its spectrum, on its dynamical properties). In particular, we study for a large class of symbols φ if the associated composition operator has a minimal commutant.

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• Commutants of composition operators on function spaces of several complex variables

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