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Matematicheskie Zametki, 2013, Volume 93, Issue 2, Pages 172–178
DOI: https://doi.org/10.4213/mzm10158
(Mi mzm10158)
 

This article is cited in 11 scientific papers (total in 11 papers)

Luzin's Correction Theorem and the Coefficients of Fourier Expansions in the Faber–Schauder System

M. G. Grigoryana, V. G. Krotovb

a Yerevan State University
b Belarusian State University, Minsk
References:
Abstract: Suppose that $b_n\downarrow0$ and $\sum_{n=1}^{\infty}({b_n}/{n})=+\infty$. 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 $\widetilde{f}$ so that the nonzero moduli $|A_n(\widetilde{f}\mspace{4mu})|$ of the Fourier–Faber–Schauder coefficients of the corrected function are $b_n$.
Keywords: Luzin's correction theorem, Faber–Schauder system, correcting function, Faber–Schauder spectrum.
Received: 02.12.2011
English version:
Mathematical Notes, 2013, Volume 93, Issue 2, Pages 217–223
DOI: https://doi.org/10.1134/S0001434613010239
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: M. G. Grigoryan, V. G. Krotov, “Luzin's Correction Theorem and the Coefficients of Fourier Expansions in the Faber–Schauder System”, Mat. Zametki, 93:2 (2013), 172–178; Math. Notes, 93:2 (2013), 217–223
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm10158
  • https://www.mathnet.ru/eng/mzm/v93/i2/p172
  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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