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Luzin’s correction theorem and the coefficients of Fourier expansions in the Faber-Schauder system

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Abstract

Suppose that b n ↓ 0 and Σ ∞ n=1 (b n /n)=+∞. In this paper, it is proved that any measurable almost everywhere finite function on [0, 1] can be corrected on a set of arbitrarily small measure to a continuous function \(\tilde f\) so that the nonzero moduli \(|A_n (\tilde f)|\) of the Fourier-Faber-Schauder coefficients of the corrected function are b n .

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Authors and Affiliations

  1. Yerevan State University, Yerevan, Armenia

    M. G. Grigoryan

  2. Belorussian State University, Belorussian, Russia

    V. G. Krotov

Authors
  1. M. G. Grigoryan
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  2. V. G. Krotov
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Correspondence to M. G. Grigoryan.

Additional information

Original Russian Text © M. G. Grigoryan, V. G. Krotov, 2013, published in Matematicheskie Zametki, 2013, Vol. 93, No. 2, pp. 172–178.

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Grigoryan, M.G., Krotov, V.G. Luzin’s correction theorem and the coefficients of Fourier expansions in the Faber-Schauder system. Math Notes 93, 217–223 (2013). https://doi.org/10.1134/S0001434613010239

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  • DOI: https://doi.org/10.1134/S0001434613010239

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