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This article is cited in 2 scientific papers (total in 2 papers)
The Fourier–Faber–Schauder series unconditionally divergent in measure
M. G. Grigoryana, A. A. Sargsyanb a Yerevan State University, Yerevan, Armenia
b Russian-Armenian University, Yerevan, Armenia
Abstract:
We prove that, for every $\varepsilon\in (0,1)$, there is a measurable set $E\subset[0,1]$ whose measure $|E|$ satisfies the estimate $|E|>1-\varepsilon$ and, for every function $f\in C_{[0,1]}$, there is $\tilde f\in C_{[0,1]}$ coinciding with $f$ on $E$ whose expansion n the Faber–Schauder system diverges in measure after a rearrangement.
Keywords:
uniform convergence, Faber–Schauder system, convergence in measure.
Received: 11.12.2017
Citation:
M. G. Grigoryan, A. A. Sargsyan, “The Fourier–Faber–Schauder series unconditionally divergent in measure”, Sibirsk. Mat. Zh., 59:5 (2018), 1057–1065; Siberian Math. J., 59:5 (2018), 835–842
Linking options:
https://www.mathnet.ru/eng/smj3028 https://www.mathnet.ru/eng/smj/v59/i5/p1057
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Abstract page: | 299 | Full-text PDF : | 54 | References: | 43 | First page: | 2 |
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