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<p>We study Wilson’s functional equation with an anti-endomorphism on semigroups and derive its optimal links to d’Alembert’s functional equation. As an application, we solve d’Alembert’s functional equation on semigroups with both an involutive endomorphism and an anti-endomorphism.</p>

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Finer results on Wilson functions with an anti-endomorphism on semigroups

  • 期刊论文

  • 发表日期：

    2025年5月28日

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  • Mohamed Ayoubi,
  • Driss Zeglami,
  • Ayoub Ouhabi

摘要

We study Wilson’s functional equation with an anti-endomorphism on semigroups and derive its optimal links to d’Alembert’s functional equation. As an application, we solve d’Alembert’s functional equation on semigroups with both an involutive endomorphism and an anti-endomorphism.