Extensions of the Sine Addition Formula on Monoids

TY - JOUR

T1 - Extensions of the Sine Addition Formula on Monoids

AU - Ebanks, Bruce

AU - Stetkær, Henrik

PY - 2018/9/1

Y1 - 2018/9/1

N2 - It is known that a pair (f, g) of functions with f≠ 0 satisfies the sine addition formula f(xy) = f(x) g(y) + g(x) f(y) on a semigroup only if g= (μ1+ μ2) / 2 where μ1 and μ2 are multiplicative functions. Here we solve the variant f(xy) = g1(x) h1(y) + g(x) h2(y) for four unknown functions f, g1, h1, h2 on a monoid, where g is not simply the average of two multiplicative functions but more generally a linear combination of n≥ 2 distinct multiplicative functions.

AB - It is known that a pair (f, g) of functions with f≠ 0 satisfies the sine addition formula f(xy) = f(x) g(y) + g(x) f(y) on a semigroup only if g= (μ1+ μ2) / 2 where μ1 and μ2 are multiplicative functions. Here we solve the variant f(xy) = g1(x) h1(y) + g(x) h2(y) for four unknown functions f, g1, h1, h2 on a monoid, where g is not simply the average of two multiplicative functions but more generally a linear combination of n≥ 2 distinct multiplicative functions.

KW - character

KW - functional equation

KW - multiplicative function

KW - Sine addition formula

KW - topological semigroup

UR - http://www.scopus.com/inward/record.url?scp=85051933092&partnerID=8YFLogxK

U2 - 10.1007/s00025-018-0880-z

DO - 10.1007/s00025-018-0880-z

M3 - Journal article

AN - SCOPUS:85051933092

SN - 1422-6383

VL - 73

JO - Results in Mathematics

JF - Results in Mathematics

IS - 3

M1 - 119

ER -