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Using Aichinger's equation to characterize polynomial functions (2207.08248v2)
Published 17 Jul 2022 in math.CA
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.
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