Existence of nontrivial solutions of linear functional equations - Kiss, Gergely; Varga, Adrienn (Aequationes mathematicae, 2014)
In this paper we study the functional equation ∑ i = 1 n a i f ( b i x + c i h ) = 0 ( x , h ∈ C ) where a i , b i , c i are fixed complex numbers and f : C → C is the unknown function. We show, that if there is i such that b i / c i ≠ b j / c j holds for any 1 ≤ j ≤ n , j ≠ i , the functional equation has a nonconstant solution if and only if there are field automorphisms ϕ 1 , ... , ϕ k of C such that ϕ 1 ⋯ ϕ k is a solution of the equation.