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

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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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     author = {V. A. Skvortsov},
     title = {Example of a {Walsh} series with a~subsequence of partial sums converging everywhere to zero},
     journal = {Sbornik. Mathematics},
     pages = {471--491},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {1975},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1975_26_4_a3/}
}
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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/