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 Cet article a éte moissonné depuis la source Math-Net.Ru

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

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