# The Cholewinski-Fock space in the Slice Hyperholomorphic Setting

## TL;DR

This paper explores a family of quaternionic Fock spaces within the slice hyperholomorphic framework, extending previous models and analyzing related linear operators to deepen understanding of quaternionic functional analysis.

## Contribution

It introduces a new family of quaternionic Fock spaces inspired by Cholewinski's approach, expanding the mathematical framework of slice hyperholomorphic functions.

## Key findings

- Reobtains the known slice hyperholomorphic Fock space as a special case
- Analyzes properties of quaternionic linear operators in these spaces
- Provides a broader family of Fock spaces in the quaternionic setting

## Abstract

Inspired from the Cholewinski approach see [5], we investigate a family of Fock spaces in the quaternionic slice hyperholomorphic setting as well as some associated quaternionic linear operators. In a particular case, we reobtain the slice hyperholomorphic Fock space introduced and studied in [2].