Extensions of the sine addition law on groups

TY - JOUR

T1 - Extensions of the sine addition law on groups

AU - Stetkær, Henrik

PY - 2019

Y1 - 2019

N2 - Let G be a group, and let χ and μ be characters of G. We find the solutions of the functional equation f(xy) = f(x) χ(y) + μ(x) f(y) , x, y∈ G, where f: G→ C is the unknown function. This enables us to solve its Pexiderized version f(xy) = g(x) h1(y) + μ(x) h2(y) , x, y∈ G, in which f, g, h1, h2: G→ C are the unknown functions.

AB - Let G be a group, and let χ and μ be characters of G. We find the solutions of the functional equation f(xy) = f(x) χ(y) + μ(x) f(y) , x, y∈ G, where f: G→ C is the unknown function. This enables us to solve its Pexiderized version f(xy) = g(x) h1(y) + μ(x) h2(y) , x, y∈ G, in which f, g, h1, h2: G→ C are the unknown functions.

KW - Character

KW - FUNCTIONAL-EQUATION

KW - Functional equation

KW - Group

KW - Levi-Civita

KW - Sine addition law

UR - http://www.scopus.com/inward/record.url?scp=85050214112&partnerID=8YFLogxK

U2 - 10.1007/s00010-018-0584-1

DO - 10.1007/s00010-018-0584-1

M3 - Journal article

AN - SCOPUS:85050214112

SN - 0001-9054

VL - 93

SP - 467

EP - 484

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

IS - 2

ER -