Composition operators on spaces of double Dirichlet series

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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Correspondence to Jaime Castillo-Medina.

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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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Keywords

  • Double Dirichlet series
  • Composition operator
  • Superposition operator

Mathematics Subject Classification

  • 30B50
  • 47B33
  • 46J15
  • 32A10