функции Хаара

Same Properties r-fold Integration Series on Fourier – Haar System

Authors: Sharapudinov I. I., Muratova G. N.

Approximation properties of series obtained by r-fold integration of Fourier – Haar series are research. It is shown that r-fold integrated Fourier – Haar series can be useful in the task of simultaneous approximation of differentiable function and its derivatives.

Haar Series on Compact Zero-Dimensional Abelian Group

Authors: Lukomskii S. F.

In this article we construct a Haar system on compact zerodimensional abelian group as shifts and powers of some characters system. We find conditions under which a Fourier-Haar series of continuous function converge uniformly. We find groups for which Haar functions generated from one function by the operation of shifts, powers and dilations.

Lebesgue functions for Haar system on compact zero-dimensional group

Authors: Komissarova N. E.

 In this article we discuss Lebesgue functions for Haar system on compact zero-dimensional group. We find cases when they are constant, also we find two-sided estimates for Lebesgue functions.