Approximation by polynomials with constant coefficients and the Thresholding Greedy Algorithm

TL;DR

This paper studies greedy bases and their approximation properties, focusing on polynomial approximation with constant coefficients and extending results to quasi-Banach spaces, building on prior characterizations of these bases.

Contribution

It improves optimization problems related to polynomial approximation with constant coefficients and extends the theory of greedy bases to quasi-Banach spaces.

Findings

Enhanced understanding of greedy bases in quasi-Banach spaces

Improved optimization techniques for polynomial approximation

Extended characterization of greedy bases beyond Banach spaces

Abstract

Greedy bases are those bases where the Thresholding Greedy Algorithm (introduced by S. V. Konyagin and V. N. Temlyakov) produces the best possible approximation up to a constant. In 2017, Bern\'a and Blasco gave a characterization of these bases using polynomials with constant coefficients. In this paper, we continue this study improving some optimization problems and extending some results to the context of quasi-Banach spaces.