A generalization of d'Alembert's functional equation on semigroups

Omar Ajebbar; Elhoucien Elqorachi

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arXiv · 1907.12966

A generalization of d'Alembert's functional equation on semigroups

Omar Ajebbar·Elhoucien Elqorachi

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Abstract

Given a semigroup $S$ generated by its squares equipped with an involutive automorphism $\sigma$ and a multiplicative function $\mu:S\to\mathbb{C}$ such that $\mu(x\sigma(x))=1$ for all $x\in S$, we determine the complex-valued solutions of the following functional equation.

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Omar Ajebbar, Elhoucien Elqorachi. 2019-07-29. A generalization of d'Alembert's functional equation on semigroups. https://arxiv.org/abs/1907.12966

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