Stetkær, Henrik D’Alembert’s and Wilson’s functional equations on step 2 nilpotent groups. (English) Zbl 1054.39017 Aequationes Math. 67, No. 3, 241-262 (2004). 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. Reviewer: János Aczél (Waterloo/Ontario) Cited in 18 Documents MSC: 39B52 Functional equations for functions with more general domains and/or ranges 39B32 Functional equations for complex functions Keywords:d’Alembert functional equation; nilpotent groups; complex valued solutions; metabelian groups; Wilson’s functional equation Citations:Zbl 0959.39023 PDFBibTeX XMLCite \textit{H. Stetkær}, Aequationes Math. 67, No. 3, 241--262 (2004; Zbl 1054.39017) Full Text: DOI