More about Wilson’s functional equation

TY - JOUR

T1 - More about Wilson’s functional equation

AU - Stetkær, Henrik

PY - 2020/6

Y1 - 2020/6

N2 - Let G be a group with an involution x↦ x∗, let μ: G→ C be a multiplicative function such that μ(xx∗) = 1 for all x∈ G, and let the pair f, g: G→ C satisfy that f(xy)+μ(y)f(xy∗)=2f(x)g(y),∀x,y∈G.For G compact we obtain: If g is abelian, then f is abelian. For G nilpotent we obtain: (1) If G is generated by its squares and f≠ 0 , then g is abelian. (2) If g is abelian, but not a multiplicative function, then f is abelian.

AB - Let G be a group with an involution x↦ x∗, let μ: G→ C be a multiplicative function such that μ(xx∗) = 1 for all x∈ G, and let the pair f, g: G→ C satisfy that f(xy)+μ(y)f(xy∗)=2f(x)g(y),∀x,y∈G.For G compact we obtain: If g is abelian, then f is abelian. For G nilpotent we obtain: (1) If G is generated by its squares and f≠ 0 , then g is abelian. (2) If g is abelian, but not a multiplicative function, then f is abelian.

KW - d’Alembert

KW - Functional equation

KW - Nilpotent group

KW - Wilson

UR - http://www.scopus.com/inward/record.url?scp=85081300608&partnerID=8YFLogxK

U2 - 10.1007/s00010-019-00654-9

DO - 10.1007/s00010-019-00654-9

M3 - Journal article

AN - SCOPUS:85081300608

SN - 0001-9054

VL - 94

SP - 429

EP - 446

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

IS - 3

ER -