This article is cited in 1 paper

Fourier–Haar Coefficients and Properties of Continuous Functions

V. Tsagareishvili

Tbilisi Ivane Javakhishvili State University

Abstract: It is well known that if the Fourier–Haar coefficients have a certain order or if a certain series composed of the Fourier–Haar coefficients of a function $f(x)\in C(0,1)$ converges, then the function has a certain form. In the present paper, we prove that not only the Fourier–Haar coefficients, but also the difference of these coefficients possess these properties.

Keywords: orthonormal Haar system, Fourier–Haar coefficient, continuous function, Abel transformation, binary irrational point.

UDC: 517.521

Received: 24.10.2008
Revised: 07.07.2009

DOI: 10.4213/mzm6593

 English version: Mathematical Notes, 2010, 87:3, 416–424

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