D'Alembert's and Wilson's functional equations on step 2 nilpotent groups
The author extends his work [Aequationes Math. 59, 306--320 (2000; Zbl 0959.39023)] about complex valued solutions \(f\) of d'Alembert's functional equation \(f(x+y)+f(x-y)=2f(x)f(y)\) to complex valued solutions \(f,g\) of Wilson's equation \(f(x+y)+f(x-y)=2f(x)g(y)\) on ``step 2 nilpotent groups''. They were called metabelian groups in the previous paper and are groups whose commutator subgroup is subset of their center. These groups are chosen because they are close to abelian groups but the author offers on them solutions of the two above mentioned functional equations that are essentially different of those in the abelian case.
scientific article; zbMATH DE number 2106521
scientific article