Existence of nontrivial solutions of linear functional equations

• Published in: Aequationes mathematicae Vol. 88; no. 1-2; pp. 151 - 162
• Main Authors: Kiss, Gergely, Varga, Adrienn
• Format: Journal Article
• Language: English
• Published: Basel Springer Basel 01.09.2014; Springer Nature B.V
• Subjects: Analysis; Automorphisms; Combinatorics; Complex numbers; Functions (mathematics); Linear equations; Mathematical analysis; Mathematics; Mathematics and Statistics; Texts; Primary 39B22; Functional equations; variety; field isomorphisms

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 equat...