The Abel equation and total solvability of linear functional equations

• Autorzy: G. Belitskii , Yu. Lyubich
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

functional equation; Abel equation; cohomological equation; wandering set

Kategorie tematyczne

• 39B22: Equations for real functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 127
• Numer: 1
• Strony: 81-97

Daty

wydano

1998

otrzymano

1996-11-04

poprawiono

1997-06-17

Twórcy

autor

G. Belitskii

• Ben-Gurion University of the Negev, 84105 Beer-Sheva, Israel

autor

Yu. Lyubich

• Department of Mathematics, Technion, 32000 Haifa, Israel

Bibliografia

• [1] N. H. Abel, Détermination d'une fonction au moyen d'une équation qui ne contient qu'une seule variable, in: Oeuvres complètes, Vol. II, Christiania, 1881.
• [2] G. Belitskii and Yu. Lyubich, On the normal solvability of cohomological equations on compact topological spaces, Proc. IWOTA-95 (to appear).
• [3] M. Kuczma, Functional Equations in a Single Variable, Polish Sci. Publ., Warszawa, 1968.
• [4] Z. Nitecki, Differentiable Dynamics, MIT Press, Cambridge, Mass., 1971.
• [5] H. Whitney, Geometric Integration Theory, Princeton Univ. Press, Princeton, N.J., 1957.