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Uniform convergence of Fourier series over Vilenkin system in the case of unbounded $p_k$

S. M. Voronov

D. Mendeleev University of Chemical Technology of Russia

Abstract: Series with respect to a system of characters of a zero-dimensional compact commutative group are considered. A generalization of an analogue of Salem test and its corollaries, which were earlier obtained in the case of bounded sequence $\{p_k\}$ defining the system, are proved.

Key words: zero-dimensional group, characters of a group, Fourier series, Salem test, Vilenkin system.

UDC: 517.518.43

Received: 22.11.2019
Revised: 03.09.2021

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2022, 77:1, 41–45

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