Wilson's functional equation on \(\mathbb{C}\)
The author obtains the solutions of the Wilson functional equation \[ \frac{1}{N} \sum^{N-1}_{n=0} f(x+w^ny)= f(x)g(y), \qquad x,y\in\mathbb{C}, \] by relating its solutions to two other equations \[ \frac{1}{N} \sum^{N-1}_{n=0} f(x+w^ny) w^{nr}= g(x)f(y), \qquad x,y\in\mathbb{C}, \] and \[ \frac{1}{N} \sum^{N-1}_{n=0} g(x+w^n y)=g(x)g(y), \qquad x,y\in\mathbb{C}, \] where \(w^N=1\) and \(w^m\neq 1\) for \(m=1,2,\dots, N-1\), \(r=0,1,\dots, N-1\).
scientific article; zbMATH DE number 988014
scientific article