Geodesic
On Best Convergence of Series in the Systems $\varphi(nx)$
Matematičeskie zametki, Tome 98 (2015) no. 4, pp. 565-569.

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

Sufficient conditions for the best convergence in $L_p$ of series in systems $\varphi(nx)$, where $\varphi(x)$ are polynomials or series in trigonometric and Walsh systems, are obtained.
Mots-clés : best convergence
Keywords: trigonometric series, Walsh series, Paley series, Banach space. 
@article{MZM_2015_98_4_a6,
     author = {A. I. Rubinshtein},
     title = {On {Best} {Convergence} of {Series} in the {Systems} $\varphi(nx)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {565--569},
     publisher = {mathdoc},
     volume = {98},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_4_a6/}
}
TY  - JOUR
AU  - A. I. Rubinshtein
TI  - On Best Convergence of Series in the Systems $\varphi(nx)$
JO  - Matematičeskie zametki
PY  - 2015
SP  - 565
EP  - 569
VL  - 98
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_98_4_a6/
LA  - ru
ID  - MZM_2015_98_4_a6
ER  - 
%0 Journal Article
%A A. I. Rubinshtein
%T On Best Convergence of Series in the Systems $\varphi(nx)$
%J Matematičeskie zametki
%D 2015
%P 565-569
%V 98
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2015_98_4_a6/
%G ru
%F MZM_2015_98_4_a6
A. I. Rubinshtein. On Best Convergence of Series in the Systems $\varphi(nx)$. Matematičeskie zametki, Tome 98 (2015) no. 4, pp. 565-569. http://geodesic.mathdoc.fr/item/MZM_2015_98_4_a6/

[1] S. N. Bernshtein, “O periodicheskikh funktsiyakh, dlya kotorykh nailuchshe skhodyaschimsya ryadom yavlyaetsya ryad Fure”, Trudy Leningradskogo industrialnogo instituta. Ser. 3. Fiz.-matem. nauki, 10:3 (1936), 3–8

[2] S. B. Stechkin, “Nailuchshie priblizheniya funktsii, predstavimykh lakunarnymi trigonometricheskimi ryadami”, Dokl. AN SSSR, 76 (1951), 33–36 | MR | Zbl

[3] A. I. Rubinshtein, “O nailuchshe skhodyaschikhsya ryadakh”, Doklady rasshirennykh zasedanii seminara Instituta prikladnoi matematiki im. I. N. Vekua, 1, no. 2, Tbilisi, 1985, 114–117

[4] A. I. Rubinshtein, “O nailuchshe skhodyaschikhsya $L_p[0,2\pi]$ ryadakh”, Matem. zametki, 52:6 (1992), 100–108 | MR | Zbl

[5] S. M. Nikolskii, “Priblizhenie funktsii trigonometricheskimi polinomami v srednem”, Izv. AN SSSR. Ser. matem., 10:3 (1946), 207–256 | MR | Zbl

[6] I. Zinger, “Caractérisation des éléments de meilleure approximation dans un espace de Banach quelconque”, Acta Sci. Math. Szeged, 17 (1956), 181–189 | MR

[7] A. I. Rubinshtein, “O nailuchshei skhodimosti”, Matem. sb., 192:2 (2001), 119–138 | DOI | MR | Zbl

[8] A. I. Rubinshtein, “O modulyakh nepreryvnosti i nailuchshikh priblizheniyakh v $L_p$ funktsii, predstavimykh lakunarnymi ryadami Uolsha”, Izv. vuzov. Matem., 1983, no. 5, 61–68 | MR | Zbl