Paley-Wiener Theorems For Slice Regular Functions

TL;DR

This paper extends classical Paley-Wiener theorems to the setting of slice regular functions, providing new tools for analysis and applications in quaternionic function theory.

Contribution

It proves two Paley-Wiener theorems for slice regular functions and derives a reproducing kernel and sampling theorem in this context.

Findings

Established Paley-Wiener theorems for slice regular functions

Computed the reproducing kernel for the slice regular Paley-Wiener space

Derived a sampling theorem for these functions

Abstract

We prove two theorems of Paley and Wiener in the slice regular setting. As an application, we can compute the reproducing kernel for the slice regular Paley-Wiener space, and obtain a related sampling theorem.