Exponential polynomials and the sine addition law on magmas

Henrik Stetkær*

*Corresponding author for this work

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

Abstract

For any set X we let F(X) denote the complex vector space of functions f: X→ C . Let X= S be a magma, and let V be a subspace of F(S) , which is invariant under left or right translations. It is known for an abelian group S that if p1χ1, ⋯ , pnχn∈ F(S) are nonzero exponential polynomials with distinct exponentials χ1, ⋯ , χn then p1χ1+ ⋯ + pnχn∈ V⇒ p1χ1, ⋯ , pnχn∈ V and χ1, ⋯ , χn∈ V . We extend this to magmas. Our results imply that any exponential polynomial solution f∈ F(S) of f(xy) = f(x) χ(y) + χ(x) f(y) where χ∈ F(S) is an exponential, has the form f= aχ where a∈ F(S) is additive, even when χ has zeros.

Original languageEnglish
JournalAequationes Mathematicae
Volume97
Issue5-6
Pages (from-to)963-979
Number of pages17
ISSN0001-9054
DOIs
Publication statusPublished - Dec 2023

Keywords

  • Exponential
  • Exponential polynomial
  • Levi–Civita
  • Magma
  • Sine addition law

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