Geodesic
On systems of convergence
Sbornik. Mathematics, Tome 10 (1970) no. 1, pp. 21-36 
E. M. Nikishin. On systems of convergence. Sbornik. Mathematics, Tome 10 (1970) no. 1, pp. 21-36. http://geodesic.mathdoc.fr/item/SM_1970_10_1_a1/
@article{SM_1970_10_1_a1,
     author = {E. M. Nikishin},
     title = {On~systems of convergence},
     journal = {Sbornik. Mathematics},
     pages = {21--36},
     year = {1970},
     volume = {10},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_10_1_a1/}
}
TY  - JOUR
AU  - E. M. Nikishin
TI  - On systems of convergence
JO  - Sbornik. Mathematics
PY  - 1970
SP  - 21
EP  - 36
VL  - 10
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1970_10_1_a1/
LA  - en
ID  - SM_1970_10_1_a1
ER  - 
%0 Journal Article
%A E. M. Nikishin
%T On systems of convergence
%J Sbornik. Mathematics
%D 1970
%P 21-36
%V 10
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1970_10_1_a1/
%G en
%F SM_1970_10_1_a1

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

In this paper we shall give necessary and sufficient conditions for a system of measurable functions to be a system of convergence, in various senses of this expression. Sharper results will be given for systems $\{\varphi(nx)\}$. Bibliography: 6 titles.

[1] W. Orlicz, “Über die Divergenz von allgemeinen Orthogonalreihen”, Studia Math., 4 (1933), 27–37

[2] P. P. Khalmosh, Lektsii po ergodicheskoi teorii, IL, Moskva, 1959

[3] E. M. Nikishin, “Rezonansnye teoremy dlya funktsionalnykh ryadov i posledovatelnostei”, DAN SSSR, 186:4 (1969), 773–775 | Zbl

[4] E. M. Nikishin, “O skhodimosti nekotorykh funktsionalnykh ryadov”, Izv. AN SSSR, seriya matem., 31:1 (1967), 15–26 | Zbl

[5] S. Kachmazh, G. Shteingauz, Teoriya ortogonalnykh ryadov, Fizmatgiz, Moskva, 1958

[6] E. M. Nikishin, “O sistemakh absolyutnoi skhodimosti”, Matem. sb., 74(116) (1967), 544–553 | Zbl