This article is cited in 1 paper

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.

UDC: 517.9

Received: 08.12.1976

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

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