Uniform convergence of the greedy algorithm with respect to the Walsh system

Martin Grigoryan¹

¹ Yerevan State University 0025 Yerevan, Armenia

Studia Mathematica, Tome 198 (2010) no. 2, pp. 197-206

Résumé

For any $0 \epsilon1$, $p\geq 1$ 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.

Détail

DOI : 10.4064/sm198-2-6

Keywords: epsilon geq each function function infty mes neq epsilon its greedy algorithm respect walsh system converges uniformly sequence spec decreasing where sequence fourier coefficients respect walsh system