## 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(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 language | English |
---|---|

Journal | Aequationes Mathematicae |

Volume | 97 |

Issue | 5-6 |

Pages (from-to) | 963-979 |

Number of pages | 17 |

ISSN | 0001-9054 |

DOIs | |

Publication status | Published - Dec 2023 |

## Keywords

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