This article is cited in 2 papers

On changes of variable that preserve convergence and absolute convergence of Fourier-Haar series

K. R. Bitsadze

Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia

Abstract: It is established that among all the differentiable homeomorphic changes of variable only the functions $\varphi_1(x)=x$ and $\varphi_2(x)=1-x$ for $x\in[0,1]$ preserve convergence everywhere of the Fourier-Haar series. The same is true for absolute convergence everywhere.
Bibliography: 8 titles.

Keywords: Fourier-Haar series, changes of variable.

UDC: 517.518.45

MSC: 42C10

Received: 01.11.2017 and 31.07.2018

DOI: 10.4213/sm9033

 English version: Sbornik: Mathematics, 2019, 210:6, 783–808

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