Rate of convergence of Thresholding Greedy Algorithms

Abstract

The rate of convergence of the classical Thresholding Greedy Algorithm with respect to some bases is studied. We bound the error of approximation by the product of two norms, the norm of $f$ and the $A_1$-norm of $f$. We obtain some results for greedy bases, unconditional bases and quasi-greedy bases. In particular, we prove that our bounds for the trigonometric basis and Haar basis are optimal. Bibliography: 16 titles.