Characterizations of eigenspaces by functional equations (Q704872)

The authors consider a linear one-to-one operator \(F\) defined on a real vector space. They motivate the study of that operator as follows: 1. \(F\) generates classical continuous nowhere differentiable functions from very simple ones. 2. \(F\) occurs in Hyer-Ulam's stability theory. 3. \(F\) is strongly connected with iterative functional equations. Among other results they characterize eigenspaces of the restrictions of the considered operator to some subspaces of the vector space on which the operator \(F\) is defined. The paper is devoted to Prof. János Aczél on occasion of his 80th birthday.