Description

• Title:
  Sine subtraction laws on semigroups
• Creator:
  Ebanks, Bruce
• Description:
  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.
• Object availability:
  free access
• Date:
  2023.02.07
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Annales Mathematicae Silesianae; Vol. 37 No. 1 (2023); 49-66;
  Annales Mathematicae Silesianae; Tom 37 Nr 1 (2023); 49-66;
  2391-4238;
  0860-2107
• Format:
  application/pdf
• Publisher:
  University of Silesia Press
• Relation: https://journals.us.edu.pl/index.php/AMSIL/article/view/15209/11682
• Subject:
  sine subtraction law;
  semigroup;
  homomorphic involution;
  antihomomorphic involution;
  topological semigroup
• Identifier: https://journals.us.edu.pl/index.php/AMSIL/article/view/15209
• Data provider:
  Czasopisma Wydawnictwa Uniwersytetu Śląskiego
• Can I use it?:
  seek permission
• Type:
  other