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Mat. Zametki, 1978, Volume 23, Issue 3, Pages 463–470 (Mi mz8161)  

Homological equations and topological properties of $S^1$-extensions over an ergodic rotation of the circle

A. A. Gura

Tula Polytechnical Institute

Abstract: 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.

Full text: PDF file (608 kB)

English version:
Mathematical Notes, 1978, 23:3, 251–255

Bibliographic databases:

UDC: 517.9
Received: 08.12.1976

Citation: A. A. Gura, “Homological equations and topological properties of $S^1$-extensions over an ergodic rotation of the circle”, Mat. Zametki, 23:3 (1978), 463–470; Math. Notes, 23:3 (1978), 251–255

Citation in format AMSBIB
\Bibitem{Gur78}
\by A.~A.~Gura
\paper Homological equations and topological properties of $S^1$-extensions over an ergodic rotation of the circle
\jour Mat. Zametki
\yr 1978
\vol 23
\issue 3
\pages 463--470
\mathnet{http://mi.mathnet.ru/mz8161}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=473142}
\zmath{https://zbmath.org/?q=an:0424.54033|0412.54048}
\transl
\jour Math. Notes
\yr 1978
\vol 23
\issue 3
\pages 251--255
\crossref{https://doi.org/10.1007/BF01651441}


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