2013; Physical and Mathematical Sciences, 47(3 (232): 23–28
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ON A PROPERTY OF GENERAL HAAR SYSTEM

A.Kh. Kobelyan*

Received: 2025-02-17 · Published: 2013-11-20

© 2013 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
ON A PROPERTY OF GENERAL HAAR SYSTEM
Author
A.Kh. Kobelyan
Published
2013-11-20
Licence
Creative Commons Attribution 4.0 International

Abstract

In the paper we prove that for some type of general Haar systems (particularly for classical Haar system) and for any ε>0 there exists a set {E⊂(0,1)2,|E|>1−ε}, such that for every f∈L1(0,1)2 one can find a function g∈L1(0,1)2, which coincides with f on E and Fourier--Haar coefficients {c(i,k)(g)}i,k=1∞ are monotonic over all rays.
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