Contreras Márquez, Manuel DomingoGómez Cabello, CarlosRodríguez Piazza, Luis2023-08-302023-08-302023Contreras Márquez, M.D., Gómez Cabello, C. y Rodríguez Piazza, L. (2023). Semigroups of composition operators on Hardy spaces of Dirichlet series. Journal of Functional Analysis, 285 (9), 110089. https://doi.org/10.1016/j.jfa.2023.110089.0022-1236https://hdl.handle.net/11441/148558This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).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:C+→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 G and strongly continuous semigroups of composition operators {Tt}t≥0, where Tt(f)=f∘Φt, f∈H2. 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 G as those Dirichlet series sending C+ into its closure. Some dynamical properties of the semigroups are obtained from a description of the Koenigs map of the semigroup.application/pdf36 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Semigroups of composition operatorsHardy spaces of Dirichlet seriesinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.jfa.2023.110089