Fock and Hardy spaces: Clifford Appell case

Daniel Alpay, Kamal Diki, Irene Sabadini

Research output: Contribution to journalArticlepeer-review


In this paper, we study a specific system of Clifford–Appell polynomials and, in particular, their product. Moreover, we introduce a new family of quaternionic reproducing kernel Hilbert spaces in the framework of Fueter regular functions. The construction is based on a general idea which allows us to obtain various function spaces by specifying a suitable sequence of real numbers. We focus on the Fock and Hardy cases in this setting, and we study the action of the Fueter mapping and its range.

Original languageEnglish
Pages (from-to)834-860
Number of pages27
JournalMathematische Nachrichten
Issue number5
StatePublished - 1 May 2022
Externally publishedYes


  • Appell system
  • Fock space
  • Fueter mapping
  • Hardy space
  • hypercomplex derivative
  • quaternions
  • reproducing kernels
  • shift operator

ASJC Scopus subject areas

  • Mathematics (all)


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