On behavior of Fourier coefficients by Walsh system
- Authors: Grigoryan M.G.1, Navasardyan K.A.1
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Affiliations:
- Yerevan State University
- Issue: Vol 51, No 1 (2016)
- Pages: 21-33
- Section: Real and Complex Analysis
- URL: https://journals.rcsi.science/1068-3623/article/view/227882
- DOI: https://doi.org/10.3103/S1068362316010039
- ID: 227882
Cite item
Abstract
The paper proves that for any ε > 0 there exists ameasurable set E ⊂ [0, 1] with measure |E| > 1 − ε such that for each f ∈ L1[0, 1] there is a function \(\tilde f \in {L^1}\left[ {0,1} \right]\) coinciding with f on E whose Fourier-Walsh series converges to \(\tilde f\) in L1[0, 1]-norm, and the sequence \(\left\{ {\left| {{c_k}\left( {\tilde f} \right)} \right|} \right\}_{n = 0}^\infty \) is monotonically decreasing, where \(\left\{ {{c_k}\left( {\tilde f} \right)} \right\}\) is the sequence of Fourier-Walsh coefficients of \(\left\{ {\left| {{c_k}\left( {\tilde f} \right)} \right|} \right\}_{n = 0}^\infty \).
About the authors
M. G. Grigoryan
Yerevan State University
Author for correspondence.
Email: gmarting@ysu.am
Armenia, Yerevan
K. A. Navasardyan
Yerevan State University
Email: gmarting@ysu.am
Armenia, Yerevan