A Levi–Civita functional equation on semigroups

Henrik Stetkær

doi:10.1007/s00010-021-00865-z

A Levi–Civita functional equation on semigroups

^*Corresponding author for this work

Department of Mathematics

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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.

Original language	English
Journal	Aequationes Mathematicae
Volume	96
Pages (from-to)	115-127
ISSN	0001-9054
DOIs	https://doi.org/10.1007/s00010-021-00865-z
Publication status	Published - Feb 2022

Keywords

Functional equation
Levi–Civita
Semigroup
Sine addition law

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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.",

keywords = "Functional equation, Levi–Civita, Semigroup, Sine addition law",

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T1 - A Levi–Civita functional equation on semigroups

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PY - 2022/2

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N2 - 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.

AB - 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.

KW - Functional equation

KW - Levi–Civita

KW - Semigroup

KW - Sine addition law

U2 - 10.1007/s00010-021-00865-z

DO - 10.1007/s00010-021-00865-z

M3 - Journal article

AN - SCOPUS:85122259316

SN - 0001-9054

VL - 96

SP - 115

EP - 127

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

ER -

A Levi–Civita functional equation on semigroups

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Keywords

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