Geodesic
On a property of general Haar system
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2013), pp. 23-28

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In the paper we prove that for some type of general Haar systems (particularly for classical Haar system) and for any $\varepsilon>0$ there exists a set $E\subset(0,1)^2 , | E |>1-\varepsilon$, such that for every $f\in L^1(0,1)^2$ one can find a function $g\in L^1(0,1)^2$, which coincides with $f$ on $E$ and Fourier – Haar coefficients $\{c_{(i,k)}(g)\}_{i,k=1}^{\infty}$ are monotonic over all rays.
Keywords: general Haar system
Mots-clés : convergence, Fourier–Haar coefficients. 
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A. Kh. Kobelyan. On a property of general Haar system. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2013), pp. 23-28. http://geodesic.mathdoc.fr/item/UZERU_2013_3_a3/