Using Aichinger's equation to characterize polynomial functions
Classical Analysis and ODEs
2022-11-22 v2
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 Fr\'echet's unmixed functional equation.
Cite
@article{arxiv.2207.08248,
title = {Using Aichinger's equation to characterize polynomial functions},
author = {J. M. Almira},
journal= {arXiv preprint arXiv:2207.08248},
year = {2022}
}
Comments
6 pages, submitted to a Journal