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

General Mathematics 2019-07-31 v1

Abstract

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

Keywords

Cite

@article{arxiv.1907.12966,
  title  = {A generalization of d'Alembert's functional equation on semigroups},
  author = {Omar Ajebbar and Elhoucien Elqorachi},
  journal= {arXiv preprint arXiv:1907.12966},
  year   = {2019}
}

Comments

16 pages

R2 v1 2026-06-23T10:34:53.199Z