A Levi–Civita functional equation on semigroups

Henrik Stetkær*

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

Abstract

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.

OriginalsprogEngelsk
TidsskriftAequationes Mathematicae
Vol/bind96
Sider (fra-til)115-127
ISSN0001-9054
DOI
StatusUdgivet - feb. 2022

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