компактные нуль-мерные группы

Haar Series on Compact Zero-Dimensional Abelian Group

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

 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.