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A Levi–Civita functional equation on semigroups

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Let S be a semigroup. We describe the solutions f, g: S→ C of the functional equation f(xy)=f(x)g(y)+g(x)f(y)-g(x)g(y),x,y∈S,in terms of multiplicative functions on S and solutions of the particular case φ(xy)=φ(x)χ(y)+φ(y)χ(x),x,y∈S,of the sine addition law in which χ: S→ C is a non-zero multiplicative function and φ: S→ C.

Original languageEnglish
JournalAequationes Mathematicae
Pages (from-to)115-127
Publication statusPublished - Feb 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

    Research areas

  • Functional equation, Levi–Civita, Semigroup, Sine addition law

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