**Roman Badora**

## On a Generalized Wilson Functional
Equation

**Abstract:**

We solve the functional equation

$$\sum_{n=0}^{N-1}g(x+k_{n}\cdot y)=Ng(x)f(y),\quad x,y\in G,$$

where $G$ is a locally compact Abelian group, $\{k_{0}=id_{G},k_{1},\ldots
,k_{N-1}\}$ is a finite group of continuous automorphisms of $G$, $f$ is a
bounded continuous complex-valued function on $G$ and $g$ is an almost periodic
function on $G$.

**Keywords:**

Wilson functional equation, spherical function.

**MSC 2000:** 39B32