The equation f(xy)=f(x)h(y)+g(x)f(y) and representations on C²

TY - JOUR

T1 - The equation f(xy)=f(x)h(y)+g(x)f(y) and representations on C2

AU - Stetkær, Henrik

N1 - Publisher Copyright: © The Author(s) 2023.

PY - 2024/10

Y1 - 2024/10

N2 - Let G be a topological group, and let C(G) denote the algebra of continuous, complex valued functions on G. We find the solutions f,g,h∈C(G) of the Levi-Civita equation (Formula presented.) which is an extension of the sine addition law. Representations of G on C2 play an important role. As a corollary we get the solutions f,g∈C(G) of the sine subtraction law f(xy∗)=f(x)g(y)-g(x)f(y), x,y∈G, in which x↦x∗ is a continuous involution, meaning that (xy)∗=y∗x∗ and x∗∗=x for all x,y∈G.

AB - Let G be a topological group, and let C(G) denote the algebra of continuous, complex valued functions on G. We find the solutions f,g,h∈C(G) of the Levi-Civita equation (Formula presented.) which is an extension of the sine addition law. Representations of G on C2 play an important role. As a corollary we get the solutions f,g∈C(G) of the sine subtraction law f(xy∗)=f(x)g(y)-g(x)f(y), x,y∈G, in which x↦x∗ is a continuous involution, meaning that (xy)∗=y∗x∗ and x∗∗=x for all x,y∈G.

KW - 39B32

KW - 39B52

KW - Functional equation

KW - Group

KW - Levi-Civita

KW - Representation

KW - Sine addition law

KW - Sine subtraction law

UR - http://www.scopus.com/inward/record.url?scp=85176789612&partnerID=8YFLogxK

U2 - 10.1007/s00010-023-01014-4

DO - 10.1007/s00010-023-01014-4

M3 - Journal article

AN - SCOPUS:85176789612

SN - 0001-9054

VL - 98

SP - 1419

EP - 1438

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

IS - 5

ER -