Abstract. In the present paper we are going to investigate Wilson's functional equation, where unknown functions are defined on a group and taking their values in an algebra. We express the solution of Wilson's equation in terms of absolutely convergent series of elements of a Banach algebra.

AMS Subject Classification (1991): 39B52

Keyword(s): trigonometric functions, Wilson's equation

Received May 19, 2008, and in revised form June 27, 2008. (Registered under 6065/2009.)