Matematičeskie zametki, Tome 23 (1978) no. 3, pp. 463-470
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A. A. Gura. Homological equations and topological properties of $S^1$-extensions over an ergodic rotation of the circle. Matematičeskie zametki, Tome 23 (1978) no. 3, pp. 463-470. http://geodesic.mathdoc.fr/item/MZM_1978_23_3_a13/
@article{MZM_1978_23_3_a13,
author = {A. A. Gura},
title = {Homological equations and topological properties of $S^1$-extensions over an ergodic rotation of the circle},
journal = {Matemati\v{c}eskie zametki},
pages = {463--470},
year = {1978},
volume = {23},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_3_a13/}
}
TY - JOUR
AU - A. A. Gura
TI - Homological equations and topological properties of $S^1$-extensions over an ergodic rotation of the circle
JO - Matematičeskie zametki
PY - 1978
SP - 463
EP - 470
VL - 23
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1978_23_3_a13/
LA - ru
ID - MZM_1978_23_3_a13
ER -
%0 Journal Article
%A A. A. Gura
%T Homological equations and topological properties of $S^1$-extensions over an ergodic rotation of the circle
%J Matematičeskie zametki
%D 1978
%P 463-470
%V 23
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1978_23_3_a13/
%G ru
%F MZM_1978_23_3_a13
A description is given of the set of $\beta\in[0;1]$, such that the homological equation $$ f(x+\beta)-f(x)=g(x+\alpha)-g(x) $$ has a continuous solution, where $f(x)$ is a continuous periodic function, $f(x+1)=f(x)$. The result obtained is applied in studying the property of relative separability of $S^1$-extensions over an ergodic rotation of the circle.
