On greedy algorithms with respect to generalized Walsh system

2011/09/17 by Sergo A. Episkoposian, Episkoposian, Sergo A. · 1 citation
Mathematics · #42C10 #46E30 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #Nonlinear Differential Equations Analysis #math.FA #msc:42C10 #msc:46E30

paper · pdf · doi:10.48550/arxiv.1109.3806

arxiv created 2011/09/17 · openalex publication_date 2011/09/17 · arxiv updated 2011/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we proof that there exists a function f(x) belongs to L¹[0,1] such that a greedy algorithm with regard to generalized Walsh system does not converge to f(x) in L¹[0,1] norm, i.e. the generalized Walsh system is not a quasi-greedy basis in its linear span L¹[0,1].

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