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arXiv · 2406.19737

K\"onigs maps and commutants of composition operators on the Hardy-Hilbert space of Dirichlet series

Frédéric Bayart·Xingxing Yao
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Abstract

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

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Frédéric Bayart, Xingxing Yao. 2024-06-28. K\"onigs maps and commutants of composition operators on the Hardy-Hilbert space of Dirichlet series. https://arxiv.org/abs/2406.19737

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