On the limits of indetermination and on the set of limit functions of series in the Walsh system
Sbornik. Mathematics, Tome 24 (1974) no. 2, pp. 257-265 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The main result of the article is the following Theorem. {\it If a series with respect to the Walsh system is summable $(C,1)$ on a set $E$ of positive measure to a finite function $f(t)$, the subsequence $\{S_{2^n}(t)\}$ of partial sums of this series converges almost everywhere on $E$ to the function $f(t)$.} Bibliography: 8 titles.
@article{SM_1974_24_2_a3,
     author = {L. A. Shaginyan},
     title = {On the limits of indetermination and on the set of limit functions of series in the {Walsh} system},
     journal = {Sbornik. Mathematics},
     pages = {257--265},
     year = {1974},
     volume = {24},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1974_24_2_a3/}
}
TY  - JOUR
AU  - L. A. Shaginyan
TI  - On the limits of indetermination and on the set of limit functions of series in the Walsh system
JO  - Sbornik. Mathematics
PY  - 1974
SP  - 257
EP  - 265
VL  - 24
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1974_24_2_a3/
LA  - en
ID  - SM_1974_24_2_a3
ER  - 
%0 Journal Article
%A L. A. Shaginyan
%T On the limits of indetermination and on the set of limit functions of series in the Walsh system
%J Sbornik. Mathematics
%D 1974
%P 257-265
%V 24
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1974_24_2_a3/
%G en
%F SM_1974_24_2_a3
L. A. Shaginyan. On the limits of indetermination and on the set of limit functions of series in the Walsh system. Sbornik. Mathematics, Tome 24 (1974) no. 2, pp. 257-265. http://geodesic.mathdoc.fr/item/SM_1974_24_2_a3/

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

[2] A. Zigmund, Trigonometricheskie ryady, t. 1, 2, izd-vo «Mir», Moskva, 1965 | MR

[3] G. Morgenthaler, “Walsh-Fourier series”, Trans. Amer. Math. Soc., 84:2 (1967), 472–507 | DOI | MR

[4] N. J. Fine, “Cesàro summability of Walsh-Fourier series”, Proc. Nat. Acad. Sci. USA, 41:8 (1965), 588–591 | DOI | MR

[5] P. L. Ulyanov, “O ryadakh po sisteme Khaara s monotonnymi koeffitsientami”, Izv. AN SSSR, seriya matem., 28 (1964), 925–950

[6] F. G. Arutyunyan, “O ryadakh po sisteme Khaara”, DAN Arm.SSR, 42:3 (1966), 134–140 | MR | Zbl

[7] V. A. Skvortsov, “O ryadakh Khaara, skhodyaschikhsya po podposledovatelnostyam chastichnykh summ”, DAN SSSR, 183:4 (1968), 784–786 | Zbl

[8] R. F. Gundy, “Martingal theory and pointweise convergence of certain orthogonal series”, Trans. Amer. Math. Soc., 124:2 (1966), 228–248 | DOI | MR | Zbl