Abstract
The functional equation ϕ(Fx) - ϕ(x) = γ(x) in continuous functions on a compact topological space X is considered, F: X → X is a continuous mapping. It is proved that the equation is normally solvable in C(X) if and only if F is preperiodic, i.e. F p+l = F l for some p ≥ 1, l ≥ 0. The solvability problem in measurable functions is also investigated.
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Belitskii, G., Lyubich, Y.I. (1998). On the normal solvability of cohomological equations on compact topological spaces. In: Gohberg, I., Mennicken, R., Tretter, C. (eds) Recent Progress in Operator Theory. Operator Theory Advances and Applications, vol 103. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8793-9_4
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DOI: https://doi.org/10.1007/978-3-0348-8793-9_4
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