Extensions of the sine addition law on groups

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 group, and let χ and μ be characters of G. We find the solutions of the functional equation f(xy) = f(x) χ(y) + μ(x) f(y) , x, y∈ G, where f: G→ C is the unknown function. This enables us to solve its Pexiderized version f(xy) = g(x) h1(y) + μ(x) h2(y) , x, y∈ G, in which f, g, h1, h2: G→ C are the unknown functions.

Original languageEnglish
JournalAequationes Mathematicae
Volume93
Issue2
Pages (from-to)467-484
Number of pages18
ISSN0001-9054
DOIs
Publication statusPublished - 2019

Keywords

  • Character
  • FUNCTIONAL-EQUATION
  • Functional equation
  • Group
  • Levi-Civita
  • Sine addition law

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