Quaternionic Fock space in an Euclidean unit ball $\mathbb{B}^n$

TL;DR

This paper introduces and analyzes quaternionic Fock spaces of entire slice hyperholomorphic functions within an Euclidean unit ball, extending complex Fock space theory to quaternionic settings.

Contribution

It develops the foundational theory of quaternionic Fock spaces in an Euclidean unit ball, including their basic properties and structure.

Findings

Defined quaternionic Fock spaces in the Euclidean unit ball

Established basic properties of these quaternionic spaces

Extended complex Fock space concepts to quaternionic analysis

Abstract

In this paper, we study the quaternionic counterpart of complex Fock spaces $\mathfrak{F}_{\alpha}^p ( 0<p<\infty$ and for some parameter $\alpha$) of entire slice hyperholomorphic functions in an Euclidean unit ball $\mathbb{B}^n$ in $\mathbb{H}^n.$ We also study some basic properties of these spaces.