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Functional equations in real-analytic functions

100%

Belitskii G., Tkachenko V.

Studia Mathematica

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2000

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tom 143

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nr 2

153-174

EN

The equation φ (x) = g(x,φ (x)) in spaces of real-analytic functions is considered. Connections between local and global aspects of its solvability are discussed.

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The real-analytic solutions of the Abel functional equation

100%

Belitskii G., Lyubich Y.

Studia Mathematica

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1999

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tom 134

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nr 2

135-141

XX

For the Abel equation on a real-analytic manifold a dynamical criterion of solvability in real-analytic functions is proved.

3

The Abel equation and total solvability of linear functional equations

100%

Belitskii G., Lyubich Y.

Studia Mathematica

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1998

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tom 127

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nr 1

81-97

EN

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

3 Studia Mathematica

3 Belitskii G.

2 Lyubich Y.

1 Tkachenko V.

1 2000

1 1999

1 1998

Functional equations in real-analytic functions

The real-analytic solutions of the Abel functional equation

The Abel equation and total solvability of linear functional equations