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