Quaternionic Hankel operators and approximation by slice regular functions

TL;DR

This paper investigates quaternionic Hankel operators and demonstrates their use in measuring the distance of functions from the space of bounded slice regular functions, advancing understanding in quaternionic functional analysis.

Contribution

It introduces the application of quaternionic Hankel operators to quantify the approximation of functions by slice regular functions.

Findings

Hankel operators can measure the $L^{ abla}$ distance in quaternionic spaces.

Establishes a link between Hankel operators and approximation theory in quaternionic analysis.

Provides new tools for analyzing slice regular functions in quaternionic settings.

Abstract

In this paper we study Hankel operators in the quaternionic setting. In particular we prove that they can be exploited to measure the $L^{\infty}$ distance of a slice $L^{\infty}$ function from the space of bounded slice regular functions.