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

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.1991 Mathematics Subject Classification. 41A65, 41A46, 46B15.

The weighted property (A) and the greedy algorithm

“…We denote by K u the least constant that satisfies (6), it is called the (suppression) unconditional constant, and we say that B is K u -(suppression) unconditional.…”

“…This generalization was motivated by the work of A. Cohen, R. A. DeVore and R. Hochmuth in [8]. In their recent paper [6], the first author and Ó. Blasco characterize w-greedy bases using the best m-term error in the approximation "with polynomials of constant coefficients". Moreover, [17] characterizes w-greedy bases in terms of their w-democracy and unconditionality.…”