Complete frequencies for Koenigs domains

2023/11/29 by Bracci, Filippo, Gallardo-Gutiérrez, Eva A., Yakubovich, Dmitry · 2 citations
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2311.17470

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^∞. 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^∞ (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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• From discrete iteration in the unit disc to continuous semigroups of holomorphic functions
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