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arXiv · 2311.17470

Complete frequencies for Koenigs domains

Filippo Bracci·Eva A. Gallardo-Gutiérrez·Dmitry Yakubovich
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Abstract

We provide a complete characterization of those non-elliptic semigroups of holomorphic self-maps of the unit disc for which the linear span of eigenvectors of the generator of the corresponding semigroup of composition operators is weak-star dense in $H^\infty$. We also give some necessary and some sufficient conditions for completeness in $H^p$. This problem is equivalent to the completeness of the corresponding exponential functions in $H^\infty$ (in the weak-star sense) or in $H^p$ of the Koenigs domain of the semigroup. As a tool needed for the results, we introduce and study discontinuities of semigroups of holomorphic self-maps of the unit disc.

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Filippo Bracci, Eva A. Gallardo-Gutiérrez, Dmitry Yakubovich. 2025-03-25. Complete frequencies for Koenigs domains. https://arxiv.org/abs/2311.17470

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