Exponential polynomials and the sine addition law on magmas

Henrik Stetkær*

*Corresponding author af dette arbejde

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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.

OriginalsprogEngelsk
TidsskriftAequationes Mathematicae
Vol/bind97
Nummer5-6
Sider (fra-til)963-979
Antal sider17
ISSN0001-9054
DOI
StatusUdgivet - dec. 2023

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