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On the L1-convergence and behavior of coefficients of Fourier–Vilenkin series

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Abstract

In this paper, we prove the following statement that is true for both bounded and some type of unbounded Vilenkin systems: for any \( \varepsilon \in (0,1)\), there exists a measurable set \(E\subset [0,1)\) of measure bigger than \(1-\varepsilon \) such that for any function \(f \in L^{1}[0,1)\), it is possible to find a function \(g\in L^{1}[0,1)\) coinciding with f on E, Fourier series of g with respect to Vilenkin system are convergent in \(L^{1}\)-norm and the absolute values of non zero Fourier coefficients of g are monotonically decreasing.

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Authors and Affiliations

  1. Chair of Higher Mathematics, Faculty of Physics, Yerevan State University, Alex Manoogyan Str. 1, 0025, Yerevan, Republic of Armenia

    M. G. Grigoryan & S. A. Sargsyan

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  1. M. G. Grigoryan
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  2. S. A. Sargsyan
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Correspondence to M. G. Grigoryan.

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Grigoryan, M.G., Sargsyan, S.A. On the L1-convergence and behavior of coefficients of Fourier–Vilenkin series. Positivity 22, 897–918 (2018). https://doi.org/10.1007/s11117-018-0552-y

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