TY - JOUR
T1 - The cosine addition and subtraction formulas on non-abelian groups
T2 - Addition and subtraction formulas: O. Ajebbar et al.
AU - Ajebbar, Omar
AU - Elqorachi, Elhoucien
AU - Stetkær, Henrik
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/12
Y1 - 2024/12
N2 - Let G be a topological group, and let C(G) denote the algebra of continuous, complex valued functions on G. We determine the solutions f,g,h∈C(G) of the Levi-Civita equation (Formula presented.) that extends the cosine addition law. As a corollary we obtain the solutions f,g∈C(G) of the cosine subtraction law g(xy∗)=g(x)g(y)+f(x)f(y), x,y∈G where x↦x∗ is a continuous involution of G. That x↦x∗ is an involution, means 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 determine the solutions f,g,h∈C(G) of the Levi-Civita equation (Formula presented.) that extends the cosine addition law. As a corollary we obtain the solutions f,g∈C(G) of the cosine subtraction law g(xy∗)=g(x)g(y)+f(x)f(y), x,y∈G where x↦x∗ is a continuous involution of G. That x↦x∗ is an involution, means that (xy)∗=y∗x∗ and x∗∗=x for all x,y∈G.
KW - 39B32
KW - 39B52
KW - Cosine addition law
KW - Cosine subtraction law
KW - Functional equation
KW - Group
KW - Levi–Civita
KW - Representation
UR - http://www.scopus.com/inward/record.url?scp=85189966026&partnerID=8YFLogxK
U2 - 10.1007/s00010-024-01052-6
DO - 10.1007/s00010-024-01052-6
M3 - Journal article
AN - SCOPUS:85189966026
SN - 0001-9054
VL - 98
SP - 1657
EP - 1676
JO - Aequationes Mathematicae
JF - Aequationes Mathematicae
IS - 6
ER -