Applications of Wilson's functional equation (Q1888665)

Let \(G\) be an abelian group divisible by 2 and \(F\) an algebraically closed commutative field of characteristic zero. The author offers a method for finding the general solutions \(f, g_j, h_j : G\to F\; (j=1,\dots,n)\) of the functional equation \(f(x+y)-f(x-y)=\sum^n_{j=1}g_j(x)h_j(y)\;(x,y\in G)\) in the cases \(n=1\) [done before by the author in Aequationes Math. 48, 171--193 (1994; Zbl 0811.39003)], \(n=2\) (details offered here) and \(n=3\).