Geodesic
On the uniqueness condition for the representation of functions by Walsh series
Matematičeskie zametki, Tome 21 (1977) no. 2, pp. 187-197

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We prove that if we consider a set of positive integers of a specific arithmetic nature, then a uniqueness theorem holds for the series with respect to the Walsh system with partial sums convergent with respect to a subsequence of numbers from this set. 
@article{MZM_1977_21_2_a6,
     author = {V. A. Skvortsov},
     title = {On the uniqueness condition for the representation of functions by {Walsh} series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {187--197},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_2_a6/}
}
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V. A. Skvortsov. On the uniqueness condition for the representation of functions by Walsh series. Matematičeskie zametki, Tome 21 (1977) no. 2, pp. 187-197. http://geodesic.mathdoc.fr/item/MZM_1977_21_2_a6/