Natural Sciences, Mathematics, 2026
ON A PROPERTY OF GENERAL HAAR SYSTEM
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Submitted: 2025-02-17
© 2026 by author(s) and The Gufo Inc.
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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.