A functional equation for monomial functions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929535663996928 |
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| author | Gselmann, Eszter Iqbal, Mehak |
| author_facet | Gselmann, Eszter Iqbal, Mehak |
| contents | Let $\mathbb{F}\subset \mathbb{K}$ be fields with characteristic zero, $n$ be a positive integer and $κ\in \mathbb{K}$. In this paper, we determine those monomials $f\colon \mathbb{F}\to \mathbb{K}$ of degree $n$ for which \[ f(x^{2})= κ\cdot x^{n}f(x) \] holds for all $x\in \mathbb{F}$. We show that similar to the classical results, where additive functions were considered, the monomial functions in the equation can be represented with the aid of homomorphisms and higher-order derivations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07831 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A functional equation for monomial functions Gselmann, Eszter Iqbal, Mehak Number Theory Commutative Algebra Primary 39B55, Secondary 39B72 Let $\mathbb{F}\subset \mathbb{K}$ be fields with characteristic zero, $n$ be a positive integer and $κ\in \mathbb{K}$. In this paper, we determine those monomials $f\colon \mathbb{F}\to \mathbb{K}$ of degree $n$ for which \[ f(x^{2})= κ\cdot x^{n}f(x) \] holds for all $x\in \mathbb{F}$. We show that similar to the classical results, where additive functions were considered, the monomial functions in the equation can be represented with the aid of homomorphisms and higher-order derivations. |
| title | A functional equation for monomial functions |
| topic | Number Theory Commutative Algebra Primary 39B55, Secondary 39B72 |
| url | https://arxiv.org/abs/2410.07831 |