Geodesic
The Abel equation and total solvability of linear functional equations
Studia Mathematica, Tome 127 (1998) no. 1, pp. 81-97

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We investigate the solvability in continuous functions of the Abel equation φ(Fx) - φ(x) = 1 where F is a given continuous mapping of a topological space X. This property depends on the dynamics generated by F. The solvability of all linear equations P(x)ψ(Fx) + Q(x)ψ(x) = γ(x) follows from solvability of the Abel equation in case F is a homeomorphism. If F is noninvertible but X is locally compact then such a total solvability is determined by the same property of the cohomological equation φ(Fx) - φ(x) = γ(x). The smooth situation can also be considered in this way.
DOI : 10.4064/sm-127-1-81-97
Keywords: functional equation, Abel equation, cohomological equation, wandering set

G. Belitskii 1 ; Yu. Lyubich 1

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G. Belitskii; Yu. Lyubich. The Abel equation and total solvability of linear functional equations. Studia Mathematica, Tome 127 (1998) no. 1, pp. 81-97. doi: 10.4064/sm-127-1-81-97

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