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The Abel equation and total solvability of linear functional equations

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Belitskii G., Lyubich Y.

Studia Mathematica

1998

tom 127

nr 1

81-97

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.

Ograniczanie wyników

1 Studia Mathematica

1 Belitskii G.

1 Lyubich Y.

1 1998

Wyniki wyszukiwania

The Abel equation and total solvability of linear functional equations