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

Martin Grigoryan

Studia Mathematica, Tome 196 (2010), p. 197-206 / Harvested from The Polish Digital Mathematics Library

Résumé

For any 0 < ϵ < 1, p ≥ 1 and each function $f \in L^{p} [0, 1]$ one can find a function $g \in L^{\infty} [0, 1)$ 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 $| c_{k} (g) | : k \in s p e c (g)$ is decreasing, where $c_{k} (g)$ is the sequence of Fourier coefficients of g with respect to the Walsh system.

Publié le : 2010-01-01

Zbl 1203.42046

EUDML-ID : urn:eudml:doc:285632

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-2-6,
     author = {Martin Grigoryan},
     title = {Uniform convergence of the greedy algorithm with respect to the Walsh system},
     journal = {Studia Mathematica},
     volume = {196},
     year = {2010},
     pages = {197-206},
     zbl = {1203.42046},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-2-6}
}

Martin Grigoryan. Uniform convergence of the greedy algorithm with respect to the Walsh system. Studia Mathematica, Tome 196 (2010) pp. 197-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm198-2-6/