Geodesic
Some convergence tests for Fourier series with respect to Vilenkin system in the case of unbounded $p_k$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2019), pp. 42-44 
S. M. Voronov. Some convergence tests for Fourier series with respect to Vilenkin system in the case of unbounded $p_k$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2019), pp. 42-44. http://geodesic.mathdoc.fr/item/VMUMM_2019_5_a6/
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     author = {S. M. Voronov},
     title = {Some convergence tests for {Fourier} series with respect to {Vilenkin} system in the case of unbounded $p_k$},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {42--44},
     year = {2019},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_5_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Series with respect to a system of characters of a zero-dimensional compact commutative group are considered. A generalization of the analogue of Dini test and its corollary obtained earlier for systems determined by bounded sequencees $\{p_k\}$ are proved.

[1] Vilenkin N.Ya., “Ob odnom klasse polnykh ortonormalnykh sistem”, Izv. AN SSSR. Ser. matem., 11 (1947), 363–400 | Zbl

[2] Agaev G.N., Vilenkin N.Ya., Dzhafarli G.M., Rubinshtein A.I., Multiplikativnye sistemy funktsii i analiz na nulmernykh gruppakh, Elm, Baku, 1981 | MR

[3] Dzhafarli G.M., “O skhodimosti ryadov Fure po odnomu klassu ortonormirovannykh multiplikativnykh sistem”, Izv. AN AzSSR. Seriya fiz.-matem. i tekhn. nauk, 4 (1962), 17–36 | MR | Zbl