U-set

On the Existence of Continual Closed U-set

Authors: Yurchenko I. S.

In this work we consider a system of characters of the Vilrnkin group G and study uniqueness sets for series for system of character of Vilenkin group (in other words, U-sets). We prove a sufficient condition for the U-set on the Vilenkin group and constructed continual closed U-set on the Vilenkin group.

A U-set for system of character of the zero-dimensional group under convergent over cubes

Authors: Yurchenko I. S.

 In this work we consider system of characters of the compact zero-dimensional group G and study uniqueness sets forN-fold multiple series for system of character a zero-dimensional group under convergent over cubes (in other words, U-sets). We proof that every finite set is a U-set and show that countable set with only one limit point is a U-set.