The best m-term approximation with respect to polynomials with constant coefficients

TL;DR

This paper characterizes greedy bases through their approximation error bounds when using the weak greedy algorithm with polynomials of constant coefficients, providing insights into their structure and performance.

Contribution

It introduces a new characterization of greedy bases based on error bounds involving polynomials with constant coefficients in the context of the weak greedy algorithm.

Findings

Greedy bases have uniformly bounded error terms in m-term approximations.

The paper establishes a connection between greedy bases and polynomial coefficient constraints.

Provides a framework for analyzing greedy algorithms with polynomial approximations.

Abstract

In this paper we show that that greedy bases can be defined as those where the error term using $m$-greedy approximant is uniformly bounded by the best $m$-term approximation with respect to polynomials with constant coefficients in the context of the weak greedy algorithm and weights.