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arXiv · 2210.09939

A variant of Wilson's functional equation on semigroups

Youssef Aserrar·Abdellatif Chahbi·Elhoucien Elqorachi
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Abstract

We determine the complex-valued solutions of the following functional equation \[f(xy)+\mu (y)f(\sigma (y)x) = 2f(x)g(y),\quad x,y\in S,\] where $S$ is a semigroup and $\sigma$ an automorphism, $\mu :S\rightarrow \mathbb{C}$ is a multiplicative function such that $\mu (x\sigma (x))=1$ for all $x\in S$.

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Youssef Aserrar, Abdellatif Chahbi, Elhoucien Elqorachi. 2022-10-18. A variant of Wilson's functional equation on semigroups. https://arxiv.org/abs/2210.09939

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