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

Martin Grigoryan. "Uniform convergence of the greedy algorithm with respect to the Walsh system." Studia Mathematica 198.2 (2010): 197-206. <http://eudml.org/doc/285632>.

@article{MartinGrigoryan2010,
abstract = {For any 0 < ϵ < 1, p ≥ 1 and each function $f ∈ L^\{p\}[0,1]$ one can find a function $g ∈ L^\{∞\}[0,1)$ with mesx ∈ [0,1): g ≠ f < ϵ such that its greedy algorithm with respect to the Walsh system converges uniformly on [0,1) and the sequence $\{|c_\{k\}(g)|: k ∈ spec(g)\}$ is decreasing, where $\{c_\{k\}(g)\}$ is the sequence of Fourier coefficients of g with respect to the Walsh system.},
author = {Martin Grigoryan},
journal = {Studia Mathematica},
keywords = {greedy algorithm; Walsh system},
language = {eng},
number = {2},
pages = {197-206},
title = {Uniform convergence of the greedy algorithm with respect to the Walsh system},
url = {http://eudml.org/doc/285632},
volume = {198},
year = {2010},
}

TY - JOUR
AU - Martin Grigoryan
TI - Uniform convergence of the greedy algorithm with respect to the Walsh system
JO - Studia Mathematica
PY - 2010
VL - 198
IS - 2
SP - 197
EP - 206
AB - For any 0 < ϵ < 1, p ≥ 1 and each function $f ∈ L^{p}[0,1]$ one can find a function $g ∈ L^{∞}[0,1)$ with mesx ∈ [0,1): g ≠ f < ϵ such that its greedy algorithm with respect to the Walsh system converges uniformly on [0,1) and the sequence ${|c_{k}(g)|: k ∈ spec(g)}$ is decreasing, where ${c_{k}(g)}$ is the sequence of Fourier coefficients of g with respect to the Walsh system.
LA - eng
KW - greedy algorithm; Walsh system
UR - http://eudml.org/doc/285632
ER -