Quaternionic Fock space on slice hyperholomorphic functions

TL;DR

This paper introduces quaternionic Fock spaces for slice hyperholomorphic functions, exploring their properties, growth estimates, and extending the theory of entire slice regular functions within these spaces.

Contribution

It defines new quaternionic Fock spaces for slice hyperholomorphic functions and investigates their fundamental properties and growth behavior.

Findings

Defined quaternionic Fock spaces $\

Established growth estimates for functions in these spaces

Extended the theory of entire slice regular functions in quaternionic analysis

Abstract

In this paper, we define the quaternionic Fock spaces $\mathfrak{F}_{\alpha}^p$ of entire slice hyperholomorphic functions in a quaternionic unit ball $\mathbb{B}$ in $\mathbb{H}.$ We also study growth estimate and various results of entire slice regular functions in these spaces. The work of this paper is motivated by the recent work of \cite{alpa12} and \cite{marco}.