Abstract
We study composition operators on spaces of double Dirichlet series, focusing our interest on the characterization of the composition operators of the space of bounded double Dirichlet series \({\mathcal {H}}^\infty ({\mathbb {C}}_+^2)\). We also show how the composition operators of this space of Dirichlet series are related to the composition operators of the corresponding spaces of holomorphic functions. Finally, we give a characterization of the superposition operators in \({\mathcal {H}}^\infty ({\mathbb {C}}_+)\) and in the spaces \({\mathcal {H}}^p\).
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The first author was partially supported by the Grant ANR-17-CE40-0021 of the French National Research Agency ANR (project Front). The last four authors were supported by MINECO and FEDER Project MTM2017-83262-C2-1-P. The second author was also supported by Grant FPU14/04365 and MICINN. The third and fourth authors were also supported by project Prometeo/2017/102 of the Generalitat Valenciana.
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Bayart, F., Castillo-Medina, J., García, D. et al. Composition operators on spaces of double Dirichlet series. Rev Mat Complut 34, 215–237 (2021). https://doi.org/10.1007/s13163-019-00345-8
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DOI: https://doi.org/10.1007/s13163-019-00345-8