Mathematical Notes

, Volume 93, Issue 1, pp 217–223

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

Authors

    • Yerevan State University
  • V. G. Krotov
    • Belorussian State University
Article

DOI: 10.1134/S0001434613010239

Cite this article as:
Grigoryan, M.G. & Krotov, V.G. Math Notes (2013) 93: 217. doi:10.1134/S0001434613010239

Abstract

Suppose that bn ↓ 0 and Σn=1(bn/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 bn.

Keywords

Luzin’scorrectiontheoremFaber-SchaudersystemcorrectingfunctionFaber-Schauderspectrum

Copyright information

© Pleiades Publishing, Ltd. 2013