Abstract
A description is given of the set of βεe[0;1], such that the homological equation f(x+β)−f(x)=tg (x+a)−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 S1-extensions over an ergodic rotation of the circle.
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Translated from Matematicheskie Zametki, Vol. 23, No. 3, pp. 463–470, March, 1978.
In conclusion, I thank D. V. Anosov and A. B. Katok, under whose guidance this work was carried out.
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Gura, A.A. Homological equations and topological properties of S1-extensions over an ergodic rotation of the circle. Mathematical Notes of the Academy of Sciences of the USSR 23, 251–255 (1978). https://doi.org/10.1007/BF01651441
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DOI: https://doi.org/10.1007/BF01651441