A variant of Wilson's functional equation on semigroups

2022/10/18 by Aserrar, Youssef, Chahbi, Abdellatif, Elqorachi, Elhoucien
#39B32 #39B52 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2210.09939

Abstract

We determine the complex-valued solutions of the following functional equation f(xy)+μ(y)f(σ(y)x) = 2f(x)g(y), x,y∈ S, where S is a semigroup and σ an automorphism, μ:S→ ℂ is a multiplicative function such that μ(xσ(x))=1 for all x∈ S.

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