Sine subtraction laws on semigroups

Bruce Ebanks

Published: 2023-02-07

Vol. 37 No. 1 (2023)

Sine subtraction laws on semigroups

Bruce Ebanks

Abstract

We consider two variants of the sine subtraction law on a semigroup S. The main objective is to solve f(xy^*) = f(x)g(y) - g(x)f(y) for unknown functions f,g: S→ℂ, where x↦x^* is an anti-homomorphic involution. Until now this equation was not solved even when S is a non-Abelian group and x^* = x^-1. We find the solutions assuming that f is central. A secondary objective is to solve f(xσ(y)) = f(x)g(y) - g(x)f(y), where σ: S→S is a homomorphic involution. Until now this variant was solved assuming that S has an identity element. We also find the continuous solutions of these equations on topological semigroups.

Keywords:

sine subtraction law , semigroup , homomorphic involution , antihomomorphic involution , topological semigroup

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Ebanks, B. (2023). Sine subtraction laws on semigroups. Annales Mathematicae Silesianae, 37(1), 49–66. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/15209

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Vol. 37 No. 1 (2023)
Published: 2023-03-03

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

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