Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Yurchenko I. S. Existence of a perfect U-set of multiple series over a system of characters of a zero-dimensional group convergent on cubes. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2026, vol. 26, iss. 1, pp. 28-34. DOI: 10.18500/1816-9791-2026-26-1-28-34, EDN: KKHVIQ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
02.03.2026
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Language: 
Russian
Heading: 
Mathematics
Article type: 
Article
UDC: 
517.51
DOI: 
10.18500/1816-9791-2026-26-1-28-34
EDN: 
KKHVIQ

Existence of a perfect U-set of multiple series over a system of characters of a zero-dimensional group convergent on cubes

Autors: 
Yurchenko Irina Sergeevna, Saratov State University
Abstract: 

In this work, we we consider multiple series in a character system on a zero-dimensional group. We discuss the problem of uniqueness of a multiple series with convergence on cubes. It is known that there exist non-empty perfect sets of uniqueness for multiple series in the Walsh system on a binary group with convergence on cubes. In this paper, we construct an example of a perfect set of uniqueness for multiple series in a character system of a zero-dimensional group convergent on cubes.

Key words: 
compact zero-dimensional group
сharaсters of a group
set of uniqueness
perfect set
References: 
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Received: 
19.06.2025
Accepted: 
24.10.2025
Published: 
02.03.2026
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