# Polynomial approximation in slice regular Fock spaces

## TL;DR

This paper investigates the density of polynomials in slice regular Fock spaces, providing new density results, constructive approximation methods, and quantitative estimates based on smoothness and best approximation measures.

## Contribution

It introduces new density results for polynomials in different types of slice regular Fock spaces, using constructive Taylor and convolution polynomial methods.

## Key findings

- Polynomials are dense in the considered Fock spaces.
- Constructive approximation methods are developed using Taylor expansions.
- Quantitative estimates relate approximation quality to smoothness and best approximation measures.

## Abstract

The main purpose of this paper is to prove some density results of polynomials in Fock spaces of slice regular functions. The spaces can be of two different kinds since they are equipped with different inner products and contain different functions. We treat both the cases, providing several results, some of them based on constructive methods which make use of the Taylor expansion and of the convolution polynomials. We also prove quantitative estimates in terms of higher order moduli of smoothness and in terms of the best approximation quantities.