Absolute convergence of Fourier series of functions of class $\operatorname{Lip}1$ and of functions of bounded variation
Izvestiya. Mathematics , Tome 76 (2012) no. 2, pp. 419-429.

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

We study problems of the absolute convergence of Fourier series with respect to general orthonormal systems for functions in certain classes.
Keywords: Fourier series, function of bounded variation, orthonormal system.
Mots-clés : Fourier coefficients
@article{IM2_2012_76_2_a8,
     author = {V. Sh. Tsagareishvili},
     title = {Absolute convergence of {Fourier} series of functions of class $\operatorname{Lip}1$ and of functions of bounded variation},
     journal = {Izvestiya. Mathematics },
     pages = {419--429},
     publisher = {mathdoc},
     volume = {76},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a8/}
}
TY  - JOUR
AU  - V. Sh. Tsagareishvili
TI  - Absolute convergence of Fourier series of functions of class $\operatorname{Lip}1$ and of functions of bounded variation
JO  - Izvestiya. Mathematics 
PY  - 2012
SP  - 419
EP  - 429
VL  - 76
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a8/
LA  - en
ID  - IM2_2012_76_2_a8
ER  - 
%0 Journal Article
%A V. Sh. Tsagareishvili
%T Absolute convergence of Fourier series of functions of class $\operatorname{Lip}1$ and of functions of bounded variation
%J Izvestiya. Mathematics 
%D 2012
%P 419-429
%V 76
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a8/
%G en
%F IM2_2012_76_2_a8
V. Sh. Tsagareishvili. Absolute convergence of Fourier series of functions of class $\operatorname{Lip}1$ and of functions of bounded variation. Izvestiya. Mathematics , Tome 76 (2012) no. 2, pp. 419-429. http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a8/

[1] S. Banach, “Sur la divergence des séries orthogonales”, Studia Math., 9 (1940), 139–155 | MR | Zbl

[2] G. Alexits, Convergence problems of orthogonal series, Pergamon Press, New York–Oxford–Paris, 1961 | MR | MR | Zbl | Zbl

[3] P. L. Ulyanov, “O ryadakh po sisteme Khaara”, Matem. sb., 63(105):3 (1964), 356–391 | MR | Zbl

[4] J. R. McLaughlin, “Integrated orthonormal series”, Pacific J. Math., 42 (1972), 469–475 | MR | Zbl

[5] B. I. Golubov, “O ryadakh Fure nepreryvnykh funktsii po sisteme Khaara”, Izv. AN SSSR. Ser. matem., 28:6 (1964), 1271–1296 | MR | Zbl

[6] S. V. Bochkarev, “A method of averaging in the theory of orthogonal series and some problems in the theory of bases”, Proc. Steklov Inst. Math., 146 (1980), 1–92 | MR | Zbl