On the solution of functional equations of Wilson's type on monoids.
Keywords:
Wilson's functional equation, Monoids, Multiplicative functionAbstract
Let S be a monoid, C be the set of complex numbers, and let σ,τ ∈ Antihom(S,S) satisfy τ ○ τ =σ ○ σ= id. The aim of this paper is to describe the solution ⨍,g: S → C of the functional equation
ʄ(xσ(y)) + ʄ(τ(y)x) = 2f(x)g(y), x, y ∈ S,
in terms of multiplicative and additive functions.
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