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Extensions of the Sine Addition Formula on Monoids

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Extensions of the Sine Addition Formula on Monoids. / Ebanks, Bruce; Stetkær, Henrik.

In: Results in Mathematics, Vol. 73, No. 3, 119, 01.09.2018.

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Ebanks, Bruce ; Stetkær, Henrik. / Extensions of the Sine Addition Formula on Monoids. In: Results in Mathematics. 2018 ; Vol. 73, No. 3.

Bibtex

@article{6c1f3b1ddb5b467998fa9a3b89acab93,
title = "Extensions of the Sine Addition Formula on Monoids",
abstract = "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.",
keywords = "character, functional equation, multiplicative function, Sine addition formula, topological semigroup",
author = "Bruce Ebanks and Henrik Stetk{\ae}r",
year = "2018",
month = "9",
day = "1",
doi = "10.1007/s00025-018-0880-z",
language = "English",
volume = "73",
journal = "Results in Mathematics",
issn = "1422-6383",
publisher = "Springer Basel AG",
number = "3",

}

RIS

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

VL - 73

JO - Results in Mathematics

JF - Results in Mathematics

SN - 1422-6383

IS - 3

M1 - 119

ER -