Geodesic
Example of a Divergent Fourier Series in the Vilenkin System
Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 780-787

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We construct an example of a function from the class $Lo(\sqrt{\ln^+L})$ whose Fourier–Vilenkin series diverges almost everywhere.
Keywords: Fourier series, Vilenkin system, Walsh system, Vilenkin function, Dirichlet kernel, Rademacher function. 
@article{MZM_2011_89_5_a11,
     author = {I. V. Polyakov},
     title = {Example of a {Divergent} {Fourier} {Series} in the {Vilenkin} {System}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {780--787},
     publisher = {mathdoc},
     volume = {89},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_5_a11/}
}
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I. V. Polyakov. Example of a Divergent Fourier Series in the Vilenkin System. Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 780-787. http://geodesic.mathdoc.fr/item/MZM_2011_89_5_a11/