Geodesic
Example of a Walsh series with a subsequence of partial sums converging everywhere to zero
Sbornik. Mathematics, Tome 26 (1975) no. 4, pp. 471-491 
V. A. Skvortsov. Example of a Walsh series with a subsequence of partial sums converging everywhere to zero. Sbornik. Mathematics, Tome 26 (1975) no. 4, pp. 471-491. http://geodesic.mathdoc.fr/item/SM_1975_26_4_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

An example is constructed of a Walsh series whose coefficients tend to zero, some subsequence of partial sums of which converges to zero but not all coefficients of which are zero. Bibliography: 4 titles.

[1] F. G. Arutyunyan, A. A. Talalyan, “O edinstvennosti ryadov po sistemam Khaara i Uolsha”, Izv AN SSSR, seriya matem., 28 (1964), 1391–1408 | Zbl

[2] P. L. Ulyanov, “Reshennye i nereshennye problemy teorii trigonometricheskikh i ortogonalnykh ryadov”, Uspekhi matem nauk, XIX:1(115) (1964), 3–69 | MR

[3] S. Kachmazh, G. Shteingauz, Teoriya ortogonalnykh ryadov, Fizmatgiz, M., 1958 | MR

[4] A. A. Shneider, “O edinstvennosti razlozhenii po sisteme funktsii Uolsha”, Matem. sb., 24(66) (1949), 279–300 | Zbl