Geodesic
On the existence of continual closed $U$-set
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 76-79 
I. S. Yurchenko. On the existence of continual closed $U$-set. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 76-79. http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a6/
@article{ISU_2016_16_1_a6,
     author = {I. S. Yurchenko},
     title = {On the existence of continual closed $U$-set},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {76--79},
     year = {2016},
     volume = {16},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a6/}
}
TY  - JOUR
AU  - I. S. Yurchenko
TI  - On the existence of continual closed $U$-set
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2016
SP  - 76
EP  - 79
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a6/
LA  - ru
ID  - ISU_2016_16_1_a6
ER  - 
%0 Journal Article
%A I. S. Yurchenko
%T On the existence of continual closed $U$-set
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2016
%P 76-79
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a6/
%G ru
%F ISU_2016_16_1_a6

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

In this work we consider a system of characters of the Vilrnkin group $G$ and study uniqueness sets for series for system of character of Vilenkin group (in other words, $U$-sets). We prove a sufficient condition for the $U$-set on the Vilenkin group and constructed continual closed $U$-set on the Vilenkin group.

[1] Shneider A. A., “On the uniqueness of expansions in Walsh functions”, Mat. Sb. (N.S.), 24(66):2 (1949), 279–300 (in Russian) | MR | Zbl

[2] Bokaev N. A., An uniqueness sets for some orthonormal systems, Preprint in VINITI, 03.08.1983, No 4282–83 (in Russian)

[3] Bokaev N. A., “An $U$-sets for multiplicative systems”, Vestnik Mosk. un-ta. Ser. 1. Matem. Mekh., 1995, no. 3, 84–86 (in Russian) | MR