A link between Wilson’s and d’Alembert’s functional equations

If f,g:G→C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f, g : G \to \mathbb{C}}$$\end{document}, f ≠ 0, is a solution of Wilson’s functional equation on a group G, then g is a d’Alembert function.