Ein System von Funktionalgleichungen vom verallgemeinerten Replikativitäts-Typ. (A system of functional equations of generalized replicativity type) (Q1107044)

For given functions \(g_ k:\) \({\mathbb{R}}\to {\mathbb{R}}\) the set \(R(g_ k)\) of functions f: \({\mathbb{R}}\to {\mathbb{R}}\), which are of period one, odd and satisfy the system of replicativity type \(f(x)-\sum^{k- 1}_{m=0}f((x+m)/k)=g_ k(x),\) \(k\in {\mathbb{N}}\), \(x\in {\mathbb{R}}\), is investigated. Conditions on \(g_ k\) are derived which are implied by the assumption \(R(g_ k)\neq \emptyset\). The continuous functions of \(R(g_ k)\) are characterized by their Fourier coefficients.