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More about Wilson’s functional equation

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Let G be a group with an involution x↦ x, let μ: G→ C be a multiplicative function such that μ(xx) = 1 for all x∈ G, and let the pair f, g: G→ C satisfy that f(xy)+μ(y)f(xy∗)=2f(x)g(y),∀x,y∈G.For G compact we obtain: If g is abelian, then f is abelian. For G nilpotent we obtain: (1) If G is generated by its squares and f≠ 0 , then g is abelian. (2) If g is abelian, but not a multiplicative function, then f is abelian.

Original languageEnglish
JournalAequationes Mathematicae
Volume94
Issue3
Pages (from-to)429-446
Number of pages18
ISSN0001-9054
DOIs
Publication statusPublished - Jun 2020

    Research areas

  • d’Alembert, Functional equation, Nilpotent group, Wilson

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