On the fourier-vilenkin coefficients |
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| Authors: | Martin G GRIGORYAN Stepan SARGSYAN |
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| Institution: | 1. Chair of Higher Mathematics, Faculty of Physics, Yerevan State University, Alex Manoogyan str. 1, 0025, Yerevan, Republic of Armenia;2. Chair of Higher Mathematics, Faculty of Physics, Yerevan State University, Alex Manoogyan str. 1, 0025, Yerevan, Republic of Armenia |
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| Abstract: | In this article, we prove the following statement that is true for both unbounded and bounded Vilenkin systems: for any ε ∈ (0,1), there exists a measurable set E ? 0,1) of measure bigger than 1 — ε such that for any function f ∈ L1 0,1), it is possible to find a function g ∈ L1 0,1) coinciding with f on E and the absolute values of non zero Fourier coefficients of g with respect to the Vilenkin system are monotonically decreasing. |
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| Keywords: | Vilenkin system expansions Fourier coefficients 42C10 42C20 |
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