N. A. Dyuzhina, “Density of the sums of shifts of a single function in the <nobr>$L_2^0$</nobr> space on a compact Abelian group”, Mat. Sb., 2024, Volume 215, Number 6,Pages <nobr>29

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Density of the sums of shifts of a single function in the $L_2^0$ space on a compact Abelian group

N. A. Dyuzhina^ab

^a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^b Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia

Abstract: Let $G$ be a nontrivial compact Abelian group. The following result is proved: a real-valued function on $G$ such that the sums of shifts of it are dense in the $L_{2}$-norm in the corresponding real space of mean zero functions exists if and only if the group $G$ is connected and has an infinite countable character group.
Bibliography: 13 titles.

Keywords: density, sums of shifts, compact groups, space $L_{2}$.

MSC: 41A46, 43A15

Received: 08.10.2023

DOI: 10.4213/sm10011