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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm10158https://doi.org/10.4213/mzm10158 https://www.mathnet.ru/eng/mzm/v93/i2/p172
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