Geodesic
Density of the sums of shifts of a~single function in the $L_2^0$ space on a~compact Abelian group
Sbornik. Mathematics, Tome 215 (2024) no. 6, pp. 743-754

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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 $L_{2}$. 
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     author = {N. A. Dyuzhina},
     title = {Density of the sums of shifts of a~single function in the $L_2^0$ space on a~compact {Abelian} group},
     journal = {Sbornik. Mathematics},
     pages = {743--754},
     publisher = {mathdoc},
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     number = {6},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2024_215_6_a1/}
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N. A. Dyuzhina. Density of the sums of shifts of a~single function in the $L_2^0$ space on a~compact Abelian group. Sbornik. Mathematics, Tome 215 (2024) no. 6, pp. 743-754. http://geodesic.mathdoc.fr/item/SM_2024_215_6_a1/