ON A PROPERTY OF GENERAL HAAR SYSTEM
DOI:
https://doi.org/10.46991/PYSU:A/2013.47.3.023Keywords:
general Haar system, convergence, Fourier–Haar coefficientsAbstract
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.
Downloads
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
License
Copyright (c) 2013 Proceedings of the YSU
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.