\(L^p\)-convergence of greedy algorithm by generalized Walsh system
type: Item
instance of: scholarly article
title: \(L^p\)-convergence of greedy algorithm by generalized Walsh system
zbMATH Open document ID: 1238.42011
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-03-16T00:00:00Z
full work available at URL: S0022247X12000303
review text: Let \((\psi_n)_{n=0}^\infty\) be a generalized Walsh system of order \(a\in \mathbb N\), \(a\geq 2\). The author proves two theorems. Theorem 1. Let \(p>2\). For every \(\varepsilon>0\) and \(f\in L^p(0,1)\) there is a function \(g\in L^p(0,1)\) such that \(|\{x\in[0,1]:\;g\neq f\}|<\varepsilon\) and the greedy algorithm of \(g\) converges in \(L^p\). Theorem 2. Let \(p>2\). For any \(\varepsilon>0\) and \(f\in L^p(0,1)\) there is a function \(g\in L^p(0,1)\) such that \(|\{x\in[0,1]:\;g\neq f\}|<\varepsilon\) and such that the sequence \(\{|c_k(g)|, K\in \text{spec}(g)\}\) is monotonically decreasing.
reviewed by: S. F. Lukomskii
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 6015292
zbMATH Keywords: generalized Walsh system
zbMATH Keywords: monotonic coefficients
zbMATH Keywords: greedy algorithm
author: S. A. Episkoposian
author: Martin Grigoryan
MaRDI profile type: Publication
OpenAlex ID: W2062398275
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DOI: 10.1016/J.JMAA.2012.01.014
description: scientific article; zbMATH DE number 6015292