Paley-Wiener theorems for slice monogenic functions

TL;DR

This paper establishes Paley-Wiener theorems for slice monogenic functions, enabling the analysis of various function spaces and computation of their reproducing kernels, thus advancing the understanding of these functions in mathematical analysis.

Contribution

It introduces Paley-Wiener theorems for slice monogenic functions and computes the reproducing kernels for associated function spaces, a novel extension in this area.

Findings

Proved Paley-Wiener theorems for slice monogenic function spaces

Computed reproducing kernel functions for these spaces

Enhanced understanding of the structure of slice monogenic function spaces

Abstract

In this paper, we prove some Paley-Wiener theorems for function spaces consisting of slice monogenic functions such as Paley-Wiener, Hardy and Bergman spaces. As applications, we can compute the reproducing kernel functions for the related function spaces.