On a functional equation related to an automorphism of a unit circle - Kirjackis, Eduardas (Lietuvos matematikos rinkinys, 2023)
In this article the complete description of the decisions of a functional equation(1 + ¯ζeiθ z)pf (z) = f (ω(0))f (z)is given, where ω(z) = (eiθ z + ζ )/(1 + ¯ζeiθ 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 automorpism ω(z).
Keywords: analytical function; unit circle; automorphism of unit circle