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- Title
Exponential polynomials and the sine addition law on magmas.
- Authors
Stetkær, Henrik
- 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 p 1 χ 1 , ⋯ , p n χ n ∈ F (S) are nonzero exponential polynomials with distinct exponentials χ 1 , ⋯ , χ n then p 1 χ 1 + ⋯ + p n χ n ∈ V ⇒ p 1 χ 1 , ⋯ , p n χ n ∈ V and χ 1 , ⋯ , χ n ∈ V . We extend this to magmas. Our results imply that any exponential polynomial solution f ∈ F (S) of f (x y) = f (x) χ (y) + χ (x) f (y) where χ ∈ F (S) is an exponential, has the form f = a χ where a ∈ F (S) is additive, even when χ has zeros.
- Subjects
MAGMAS; POLYNOMIALS; ABELIAN groups; BIVECTORS; FUNCTION spaces
- Publication
Aequationes Mathematicae, 2023, Vol 97, Issue 5/6, p963
- ISSN
0001-9054
- Publication type
Article
- DOI
10.1007/s00010-023-00965-y