Fock and Hardy spaces: Clifford-Appell case

TL;DR

This paper explores Clifford-Appell polynomials, introduces new quaternionic reproducing kernel Hilbert spaces, and analyzes Fock and Hardy spaces within the Fueter regular functions framework, highlighting their structure and the Fueter mapping.

Contribution

It presents a novel construction of quaternionic function spaces based on Clifford-Appell polynomials and studies their properties in the Fock and Hardy cases.

Findings

New quaternionic reproducing kernel Hilbert spaces introduced

Analysis of Fueter mapping and its range in these spaces

Characterization of Fock and Hardy spaces in this framework

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 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.