ON A PROPERTY OF GENERAL HAAR SYSTEM

Authors

  • A.Kh. Kobelyan Chair of Higher Mathematics, Faculty of Physics, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2013.47.3.023

Keywords:

general Haar system, convergence, Fourier–Haar coefficients

Abstract

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.

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Published

2013-11-20

How to Cite

Kobelyan, A. (2013). ON A PROPERTY OF GENERAL HAAR SYSTEM. Proceedings of the YSU A: Physical and Mathematical Sciences, 47(3 (232), 23–28. https://doi.org/10.46991/PYSU:A/2013.47.3.023

Issue

Section

Mathematics