Email this article The Fourier–Faber–Schauder Series Unconditionally Divergent in Measure
- Authors: Grigoryan M.G.1, Sargsyan A.A.2
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Affiliations:
- Yerevan State University
- Russian–Armenian University
- Issue: Vol 59, No 5 (2018)
- Pages: 835-842
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172031
- DOI: https://doi.org/10.1134/S0037446618050087
- ID: 172031
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Abstract
We prove that, for every ε ∈ (0, 1), there is a measurable set E ⊂ [0, 1] whose measure |E| satisfies the estimate |E| > 1−ε and, for every function f ∈ C[0,1], there is ˜ f ∈ C[0,1] coinciding with f on E whose expansion in the Faber–Schauder system diverges in measure after a rearrangement.
About the authors
M. G. Grigoryan
Yerevan State University
Author for correspondence.
Email: gmarting@ysu.am
Armenia, Yerevan
A. A. Sargsyan
Russian–Armenian University
Email: gmarting@ysu.am
Armenia, Yerevan
