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Mat. Zametki, 2013, Volume 93, Issue 2, Pages 172–178 (Mi mz10158)  

This article is cited in 6 scientific papers (total in 6 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

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.

DOI: https://doi.org/10.4213/mzm10158

Full text: PDF file (458 kB)
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English version:
Mathematical Notes, 2013, 93:2, 217–223

Bibliographic databases:

UDC: 517.5
Received: 02.12.2011

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. N. Galoyan, R. G. Melikbekyan, “Behavior of the Fourier–Walsh coefficients of a corrected function”, Siberian Math. J., 57:3 (2016), 505–512  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. M. G. Grigoryan, K. A. Navasardyan, “Universal functions in ‘correction’ problems guaranteeing the convergence of Fourier–Walsh series”, Izv. Math., 80:6 (2016), 1057–1083  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Grigoryan M.G., Navasardyan K.A., “On behavior of Fourier coefficients by Walsh system”, J. Contemp. Math. Anal.-Armen. Aca., 51:1 (2016), 21–33  crossref  mathscinet  zmath  isi  scopus
    4. M. G. Grigoryan, A. Kh. Kobelyan, “On behavior of Fourier coefficients and uniform convergence of Fourier series in the Haar system”, Adv. Oper. Theory, 3:4 (2018), 781–793  crossref  mathscinet  zmath  isi  scopus
    5. M. G. Grigoryan, A. A. Sargsyan, “The Fourier–Faber–Schauder series unconditionally divergent in measure”, Siberian Math. J., 59:5 (2018), 835–842  mathnet  crossref  crossref  isi  elib
    6. M. G. Grigoryan, “On the absolute convergence of Fourier–Haar series in the metric of $L^p(0,1)$, $0<p<1$”, J. Math. Sci. (N. Y.), 243:6 (2019), 844–858  mathnet  crossref
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