Using Aichinger's equation to characterize polynomial functions
arXiv:2207.08248
Abstract
Aichinger's equation is used to give simple proofs of several well-known characterizations of polynomial functions as solutions of certain functional equations. Concretely, we use that Aichinger's equation characterizes polynomial functions to solve, for arbitrary commutative groups, Ghurye-Olkin's functional equation, Wilson's functional equation, the Kakutani-Nagumo-Walsh functional equation, and a general version of Fréchet's unmixed functional equation.
6 pages, submitted to a Journal