The solution of the functional equation of D'Alembert's type for commutative groups

[摘要] A functional equation of the formϕ1(x+y)+ϕ2(x−y)=∑inαi(x)βi(y), where functionsϕ1,ϕ2,αi,βi,i=1,…,nare defined on a commutative group, is solved. We also obtain conditions for the solutions of this equation to be matrix elements of a finite dimensional representation of the group.

[学科分类] 数学（综合）