Geodesic
On changes of variable that preserve convergence and absolute convergence of Fourier-Haar series
Sbornik. Mathematics, Tome 210 (2019) no. 6, pp. 783-808

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2019_210_6_a1,
     author = {K. R. Bitsadze},
     title = {On changes of variable that preserve convergence and absolute convergence of {Fourier-Haar} series},
     journal = {Sbornik. Mathematics},
     pages = {783--808},
     publisher = {mathdoc},
     volume = {210},
     number = {6},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_6_a1/}
}
TY  - JOUR
AU  - K. R. Bitsadze
TI  - On changes of variable that preserve convergence and absolute convergence of Fourier-Haar series
JO  - Sbornik. Mathematics
PY  - 2019
SP  - 783
EP  - 808
VL  - 210
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2019_210_6_a1/
LA  - en
ID  - SM_2019_210_6_a1
ER  - 
%0 Journal Article
%A K. R. Bitsadze
%T On changes of variable that preserve convergence and absolute convergence of Fourier-Haar series
%J Sbornik. Mathematics
%D 2019
%P 783-808
%V 210
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2019_210_6_a1/
%G en
%F SM_2019_210_6_a1
K. R. Bitsadze. On changes of variable that preserve convergence and absolute convergence of Fourier-Haar series. Sbornik. Mathematics, Tome 210 (2019) no. 6, pp. 783-808. http://geodesic.mathdoc.fr/item/SM_2019_210_6_a1/