D'Alembert's and Wilson's equations on semigroups.

In this paper we consider a generalization of d'Alembert's equation and Wilson's equation on commutative semigroups using only the semigroup operation, ie. we consider the functional equation h (x + 2 y) + h (x) = 2 f (y) h (x + y) , x , y ∈ S , where f , h : S → K , (S , +) is a commutative semigroup, K is a quadratically closed field, char K ≠ 2 . [ABSTRACT FROM AUTHOR]