Complex Symmetry of Composition Operators on Hilbert Spaces of Entire Dirichlet Series

  • Minh Luan Doan
  • Camille Mau
  • Le Hai KhoiEmail author


A criterion for boundedness of composition operators acting on a class of Hilbert spaces of entire Dirichlet series, namely the class \(\mathcal {H}(E, \beta _{S})\), was obtained in Hou et al. (J. Math. Anal. Appl. 401: 416–429, 2013) for those spaces that do not contain non-zero constant functions, while other possibilities were not studied. In this paper, we first provide a complete characterization of boundedness of composition operators on any space \(\mathcal {H}(E, \beta _{S})\), which may or may not contain constant functions. We then study complex symmetry of composition operators on \(\mathcal {H}(E, \beta _{S})\), via analysis of composition conjugations.


Hilbert space Entire Dirichlet series Composition operator Conjugation Complex symmetry 

Mathematics Subject Classification (2010)

30E20 30D50 


Funding Information

The second-named author was supported in part by the CN Yang Scholars Programme, Nanyang Technological University. The third-named author was supported in part by MOE’s AcRF Tier 1 grant M4011724.110 (RG128/16).


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA
  2. 2.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological University (NTU)SingaporeSingapore

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