On the structure of divergence sets of Fourier-Walsh series
The author investigates the structure of the sets of divergence for some sequences of partial sums of Fourier series with respect to Walsh systems. It is proved that each set of \(G_{\delta}\) type on the dyadic group G is the set of unbounded divergence. In the class of sets of divergence for the continuous functions on G the sets which have sufficiently composite structure are indicated. Similar investigations for the trigonometrical Fourier series have been done earlier by the author [Vestn. Mosk. Univ., Ser. I 1978, No.2, 65-70 (1978; Zbl 0386.42002); ibid. 1982, No.3, 11-16 (1982; Zbl 0505.42007)].
scientific article; zbMATH DE number 3872013