On the uniqueness condition for the representation of functions by walsh series

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. Translated from Matematicheskie Zametki, Vol. 21, No. 2, pp. 187–197, February, 1977.