Abstract
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 language | English |
|---|---|
| Pages (from-to) | 834-860 |
| Number of pages | 27 |
| Journal | Mathematische Nachrichten |
| Volume | 295 |
| Issue number | 5 |
| DOIs | |
| State | Published - 1 May 2022 |
| Externally published | Yes |
Keywords
- Appell system
- Fock space
- Fueter mapping
- Hardy space
- hypercomplex derivative
- quaternions
- reproducing kernels
- shift operator
ASJC Scopus subject areas
- General Mathematics
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