Results in Mathematics

, 74:17 | Cite as

On Slice Polyanalytic Functions of a Quaternionic Variable

  • Daniel Alpay
  • Kamal Diki
  • Irene SabadiniEmail author


In this paper, we introduce the quaternionic slice polyanalytic functions and we prove some of their properties. Then, we apply the obtained results to begin the study of the quaternionic Fock and Bergman spaces in this new setting. In particular, we give explicit expressions of their reproducing kernels.


Bergman spaces Fock spaces quaternions slice polyanalytic functions 

Mathematics Subject Classification

Primary 30G35 



Kamal Diki acknowledges the support of the project INdAM Doctoral Programme in Mathematics and/or Applications Cofunded by Marie Sklodowska-Curie Actions, acronym: INdAM-DP-COFUND-2015, grant number: 713485.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Schmid College of Science and TechnologyChapman UniversityOrangeUSA
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  3. 3.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

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