Approximation by polynomials on quaternionic compact sets

TL;DR

This paper extends polynomial approximation results to quaternionic compact sets, including starlike and axially symmetric sets, with detailed cases and quantitative estimates.

Contribution

It introduces new approximation theorems for quaternionic functions on specific compact sets, expanding the classical complex approximation theory.

Findings

Approximation results for quaternionic functions on starlike sets

Approximation on axially symmetric sets with quantitative estimates

Detailed analysis of particular sets with concrete examples

Abstract

In this paper we obtain several extensions to the quaternionic setting of some results concerning the approximation by polynomials of functions continuous on a compact set and holomorphic in its interior. The results include approximation on compact starlike sets and compact axially symmetric sets. The cases of some concrete particular sets are described in details, including quantitative estimates too.