Positivity

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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.

Keywords

Vilenkin systems Convergence Fourier coefficients 

Mathematics Subject Classification

42C10 42C20 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chair of Higher Mathematics, Faculty of PhysicsYerevan State UniversityYerevanRepublic of Armenia

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