Article
Semigroups of composition operators on Hardy spaces of Dirichlet series
Author/s | Contreras Márquez, Manuel Domingo
![]() ![]() ![]() ![]() ![]() ![]() ![]() Gómez Cabello, Carlos Rodríguez Piazza, Luis ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2023 |
Deposit Date | 2023-08-30 |
Published in |
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Abstract | 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 ... 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. |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España Fondo Europeo de Desarrollo Regional (FEDER) Junta de Andalucía |
Project ID. | PGC2018-094215-13-100
![]() FQM133 ![]() FQM104 ![]() |
Citation | Contreras 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. |
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