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Sbornik: Mathematics, 2019, Volume 210, Issue 6, Pages 783–808
DOI: https://doi.org/10.1070/SM9033 (Mi sm9033) 		 
This article is cited in 2 scientific papers (total 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
English version PDF (536 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM9033
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.
Received: 01.11.2017 and 31.07.2018
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 6, Pages 30–55
DOI: https://doi.org/10.4213/sm9033
Bibliographic databases:
Document Type: Article
UDC: 517.518.45
MSC: 42C10
Language: English
Original paper language: Russian
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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  • https://www.mathnet.ru/eng/sm/v210/i6/p30
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:421
    Russian version PDF:38
    English version PDF:9
    References:49
    First page:24
     
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