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On Slice Polyanalytic Functions of a Quaternionic Variable

Results in Mathematics volume 74, Article number: 17 (2019) Cite this article

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Schmid College of Science and Technology, Chapman University, Orange, CA, 92866, USA

    Daniel Alpay

  2. Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, 20133, Milano, Italy

    Kamal Diki

  3. Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi, 9, 20133, Milano, Italy

    Irene Sabadini

Authors
  1. Daniel Alpay
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  2. Kamal Diki
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  3. Irene Sabadini
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Corresponding author

Correspondence to Irene Sabadini.

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Daniel Alpay thanks the Foster G. and Mary McGaw Professorship in Mathematical Sciences, which supported this research.

Kamal Diki is a Marie Sklodowska-Curie fellow of the Istituto Nazionale di Alta Matematica.

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Alpay, D., Diki, K. & Sabadini, I. On Slice Polyanalytic Functions of a Quaternionic Variable. Results Math 74, 17 (2019). https://doi.org/10.1007/s00025-018-0942-2

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  • DOI: https://doi.org/10.1007/s00025-018-0942-2

Mathematics Subject Classification

  • Primary 30G35

Keywords

  • Bergman spaces
  • Fock spaces
  • quaternions
  • slice polyanalytic functions