2022/02/16 by Manuel D. Contreras, Contreras, Manuel D., Carlos Gómez-Cabello +3 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2202.07969
openalex publication_date 2022/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider continuous semigroups of analytic functions \Φt\t≥0 in the so-called Gordon-Hedenmalm class G, that is, the family of analytic functions Φ:\mathbb C+→ \mathbb C+ giving rise to bounded composition operators in the Hardy space of Dirichlet series H2. We show that there is a one-to-one correspondence between continuous semigroups \Φt\t≥0 in the class \mathcal G and strongly continuous semigroups of composition operators \Tt\t≥0, where Tt(f)=f∘Φt, f\inH2. We extend these results for the range p∈[1,∞). For the case p=∞, we prove that there is no non-trivial strongly continuous semigroup of composition operators in H^∞. We characterize the infinitesimal generators of continuous semigroups in the class \mathcal G as those Dirichlet series sending \mathbb C+ into its closure. Some dynamical properties of the semigroups are obtained from a description of the Koenigs map of the semigroup.