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

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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. Grigoryan^a, V. G. Krotov^b

^a Yerevan State University
^b Belarusian State University, Minsk

Full-text PDF (458 kB) Citations (11)

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

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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Linking options:

https://www.mathnet.ru/eng/mzm10158

https://doi.org/10.4213/mzm10158

https://www.mathnet.ru/eng/mzm/v93/i2/p172

This publication is cited in the following 11 articles:

Avetisyan Zh., Grigoryan M., Ruzhansky M., “Approximations in l-1 With Convergent Fourier Series”, Math. Z., 299:3-4 (2021), 1907–1927
Grigoryan G.M., Krotov V.G., “Quasiunconditional Basis Property of the Faber-Schauder System”, Ukr. Math. J., 71:2 (2019), 237–247
Martin G. Grigoryan, Tigran M. Grigoryan, L. S. Simonyan, Springer Proceedings in Mathematics & Statistics, 275, Analysis and Partial Differential Equations: Perspectives from Developing Countries, 2019, 109
Nikolaj Mormul`, Alexander Shchitov, “A study of approximation of functions of bounded variation by Faber-Schauder partial sums”, EEJET, 4:4 (100) (2019), 14
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
M. G. Grigoryan, A. A. Sargsyan, “The Fourier–Faber–Schauder series unconditionally divergent in measure”, Siberian Math. J., 59:5 (2018), 835–842
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
Tigran Grigoryan, Martin Grigoryan, N. Mastorakis, V. Mladenov, A. Bulucea, “On the representation of signals series by Faber-Schauder system”, MATEC Web Conf., 125 (2017), 05005
L. N. Galoyan, R. G. Melikbekyan, “Behavior of the Fourier–Walsh coefficients of a corrected function”, Siberian Math. J., 57:3 (2016), 505–512
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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