On a functional equation related to an automorphism of a unit circle

• Autorzy: Kir'ytzkii E.
• Języki publikacji: EN

Abstrakty

EN

In this article the complete description of the decisions of a functional equation f(w(z)) = f(w(0))f(z) is given, where w(z)-automorphism of a unit circle E and the decisions are searched among analytical in E functions. It is established, that research of a given functional equation is closely connected to property of stationary points of automorphism w(z).

Słowa kluczowe

EN

functional equations; unit circle; omega-operator; fixed points; fixed functions

PL

równania funkcyjne; funkcja stała; dysk jednostkowy; odwzorowania

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 1
• Strony: 119--134
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Kir'ytzkii E.

• Department of Mathematics, Vilnius Gediminas Technical University, Sauletakio Str. 11, 2054 Vilnius, Lithuania

Bibliografia

• [1] G. Koenigs, Annales Ecole Norm., (3), 1, 1884 et (3), 2, 1885. (cited from G. Valizan [3]).
• [2] P. Fatou, Bull. Societe Math., 47, 1919 et 48, 1920. (cited from G. Valiron [3]).
• [3] G. Valiron, Analytical functions, Cosizdat, Moscow, 1957, p. 235 (in Russian).
• [4] Ju. V. Sidorov, M. V. Fedoriuk, M. I. Shabunin, Lectures on the theory of functions of complex variable, Moscow, “Nauka”, 1982, 488 p. (in Russia).