The Newton Product of Polynomial Projectors. Part 2 : approximation properties

TL;DR

This paper demonstrates that the Newton product of efficient polynomial projectors retains efficiency and establishes various approximation theorems across different function spaces, introducing new explicit projectors.

Contribution

It proves the preservation of efficiency in Newton product projectors and develops new explicit projectors with broad approximation properties.

Findings

Newton product of polynomial projectors remains efficient

Established approximation theorems for various function spaces

Presented new explicit polynomial projectors

Abstract

We prove that the Newton product of efficient polynomial projectors is still efficient. Various polynomial approximation theorems are established involving Newton product projectors on spaces of holomorphic functions on a neighborhood of a regular compact set, on spaces of entire functions of given growth and on spaces of differentiable functions. Efficient explicit new projectors are presented.