Uniform convergence of the greedy algorithm with respect to the Walsh system
Volume 198 / 2010
Studia Mathematica 198 (2010), 197-206
MSC: Primary 42C10; Secondary 42C20.
DOI: 10.4064/sm198-2-6
Abstract
For any $0< \epsilon<1$, $p\geq 1$ and each function $f\in L^{p}[0,1] $ one can find a function $g\in L^{\infty}[0,1)$ with ${\rm mes}\{x\in [0,1) : g\neq f\}<\epsilon$ such that its greedy algorithm with respect to the Walsh system converges uniformly on $[0,1)$ and the sequence $\{|c_{k}(g)|: k\in {\rm spec}(g)\}$ is decreasing, where $\{c_{k}(g)\}$ is the sequence of Fourier coefficients of $g$ with respect to the Walsh system.
