This article is cited in 2 papers

Mathematics

On a property of general Haar system

A. Kh. Kobelyan

Physical and Mathematical Faculty of Yerevan State University

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.

Keywords: general Haar system, convergence, Fourier–Haar coefficients.

MSC: 42C10; 42C40

Received: 23.04.2013
Accepted: 18.09.2013

Language: English