Roman Badora

On a Generalized Wilson Functional Equation

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 $G$.

Wilson functional equation, spherical function.

MSC 2000: 39B32