Almost Everywhere Convergence of Greedy Algorithm with Respect to Vilenkin System

作     者：Grigoryan, M. G. Sargsyan, S. A. 

作者机构：Yerevan State Univ Yerevan Armenia 

出 版 物：《JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES》 (当代数学分析杂志)

年 卷 期：2018年第53卷第6期

页      面：331-345页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：RAMES State Committee of Science [18T-1A148] 

主　　题：Vilenkin system convergence Fourier series greedy algorithm 

摘      要：In this paper, we prove that for any epsilon is an element of(0, 1) there exists ameasurable set E is an element of [0, 1) with measure vertical bar E vertical bar 1 - epsilon such that for any function f is an element of L-1[0, 1), it is possible to construct a function (f) over tilde L1[0,1] coinciding with f on E and satisfying integral(1)(0)vertical bar(f) over tilde (x)-f(x)vertical bar dx with respect to a bounded Vilenkin system are almost everywhere convergent on [0, 1).