On Lebesgue constants of Vilenkin systems
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2016), pp. 63-66.

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

In the paper some properties of Lebesgue constants $\left\{L_n(W)\right\}^{\infty}_{n=1}$ of Vilenkin system are investigated. Non almost convergence property for the sequence $\left\{\dfrac{L_n(W)}{\log_2n}\right\}^{\infty}_{n=2}$ is obtained.
Keywords: Vilenkin system, almost convergence.
Mots-clés : Lebesgue constants
@article{UZERU_2016_2_a10,
     author = {S. A. Sargsyan},
     title = {On {Lebesgue} constants of {Vilenkin} systems},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {63--66},
     publisher = {mathdoc},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2016_2_a10/}
}
TY  - JOUR
AU  - S. A. Sargsyan
TI  - On Lebesgue constants of Vilenkin systems
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2016
SP  - 63
EP  - 66
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2016_2_a10/
LA  - en
ID  - UZERU_2016_2_a10
ER  - 
%0 Journal Article
%A S. A. Sargsyan
%T On Lebesgue constants of Vilenkin systems
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2016
%P 63-66
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2016_2_a10/
%G en
%F UZERU_2016_2_a10
S. A. Sargsyan. On Lebesgue constants of Vilenkin systems. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2016), pp. 63-66. http://geodesic.mathdoc.fr/item/UZERU_2016_2_a10/

[1] B.I. Golubov, A.V. Efimov, V.A. Skvortsov, Walsh Series and Transforms: Theory and Applications, Kluwer Academic Publishers, Dordrecht, 1991 | MR | Zbl

[2] G.N. Agaev, N.Ya. Vilenkin, G.M. Dzhafarli, A.I. Rubinshtein, Multiplicative Systems of Functions and Harmonic Analysis on Zero-Dimensional Groups, ELM, Baku, 1981 (in Russian) | MR

[3] N.Ya. Vilenkin, “On a Class of Complete Orthonormal Systems”, Izv. Akad. Nauk SSSR, 11 (1947), 363–400 (in Russian) | MR | Zbl

[4] N.K. Bari, Trigonometric Series, Fizmatlit, M., 1961 (in Russian) | MR

[5] L. Sucheston, “Banach Limit”, Amer. Math. Monthly, 74 (1967), 308–311 | DOI | MR | Zbl

[6] S.V. Astashkin, E.M. Semenov, “Lebesgue Constants of the Walsh System”, Doklady Akademii Nauk, ser. Matematica, 91:3 (2015), 344–346 | MR | Zbl