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Published online by Cambridge University Press: 20 November 2018
Let $G$ be a compact group.
Let $\sigma$ be a continuous involution of $G$. In this paper, we are concerned by the following functional equation
where $f,g,h:G\mapsto \mathbb{C}$, to be determined, are complex continuous functions on $G$ such that $f$ is central. This equation generalizes d’Alembert's and Wilson's functional equations. We show that the solutions are expressed by means of characters of irreducible, continuous and unitary representations of the group $G$.