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arXiv · 1810.11999

Characterization of field homomorphisms through Pexiderized functional equations

Eszter Gselmann·Gergely Kiss·Csaba Vincze
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Abstract

The aim of this paper is to prove characterization theorems for field homomorphisms. More precisely, the main result investigates the following problem. Let $n\in \mathbb{N}$ be arbitrary, $\mathbb{K}$ a field and $f_{1}, \ldots, f_{n}\colon \mathbb{K}\to \mathbb{C}$ additive functions. Suppose further that equation \[ \sum_{i=1}^{n}f^{q_{i}}_{i}\left(x^{p_{i}}\right)=0 \qquad \left(x\in \mathbb{K}\right) \] is also satisfied. Then the functions $f_{1}, \ldots, f_{n}$ are linear combinations of field homomorphisms from $\mathbb{K}$ to $\mathbb{C}$.

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Eszter Gselmann, Gergely Kiss, Csaba Vincze. 2018-10-29. Characterization of field homomorphisms through Pexiderized functional equations. https://arxiv.org/abs/1810.11999

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