The cosine addition and subtraction formulas on non-abelian groups: Addition and subtraction formulas: O. Ajebbar et al.

Omar Ajebbar, Elhoucien Elqorachi, Henrik Stetkær*

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Abstract

Let G be a topological group, and let C(G) denote the algebra of continuous, complex valued functions on G. We determine the solutions f,g,h∈C(G) of the Levi-Civita equation (Formula presented.) that extends the cosine addition law. As a corollary we obtain the solutions f,g∈C(G) of the cosine subtraction law g(xy)=g(x)g(y)+f(x)f(y), x,y∈G where x↦x is a continuous involution of G. That x↦x is an involution, means that (xy)=yx and x∗∗=x for all x,y∈G.

Original languageEnglish
JournalAequationes Mathematicae
Volume98
Issue6
Pages (from-to)1657-1676
Number of pages20
ISSN0001-9054
DOIs
Publication statusPublished - Dec 2024

Keywords

  • 39B32
  • 39B52
  • Cosine addition law
  • Cosine subtraction law
  • Functional equation
  • Group
  • Levi–Civita
  • Representation

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