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Mat. Sb., 2019, Volume 210, Number 6, Pages 30–55 (Mi msb9033)  

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.

DOI: https://doi.org/10.4213/sm9033

Full text: PDF file (659 kB)
First page: PDF file
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English version:
Sbornik: Mathematics, 2019, 210:6, 783–808

Bibliographic databases:

UDC: 517.518.45
MSC: 42C10
Received: 01.11.2017 and 31.07.2018

Citation: K. R. Bitsadze, “On changes of variable that preserve convergence and absolute convergence of Fourier-Haar series”, Mat. Sb., 210:6 (2019), 30–55; Sb. Math., 210:6 (2019), 783–808

Citation in format AMSBIB
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