Characterization of polynomials by their invariance properties
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912387692494848 |
|---|---|
| author | Amira, J. M. Hu, Ya-Qing |
| author_facet | Amira, J. M. Hu, Ya-Qing |
| contents | We prove that certain classical groups $G\subseteq {\rm GL}(d,\mathbb{R}^d)$ serve to characterize ordinary polynomials in $d$ real variables as elements of finite-dimensional subspaces of $C(\mathbb{R}^d)$ that are invariant by changes of variables induced by translations and elements of $G$. We also show that, if the field $\mathbb{K}$ has characteristic $0$, the elements of $\mathbb{K}[x_1,\cdots,x_d]$ admit a similar characterization for $G= {\rm GL}(d,\mathbb{K})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of polynomials by their invariance properties Amira, J. M. Hu, Ya-Qing Classical Analysis and ODEs Group Theory 39B05, 39B22, 39B52, 39A70 We prove that certain classical groups $G\subseteq {\rm GL}(d,\mathbb{R}^d)$ serve to characterize ordinary polynomials in $d$ real variables as elements of finite-dimensional subspaces of $C(\mathbb{R}^d)$ that are invariant by changes of variables induced by translations and elements of $G$. We also show that, if the field $\mathbb{K}$ has characteristic $0$, the elements of $\mathbb{K}[x_1,\cdots,x_d]$ admit a similar characterization for $G= {\rm GL}(d,\mathbb{K})$. |
| title | Characterization of polynomials by their invariance properties |
| topic | Classical Analysis and ODEs Group Theory 39B05, 39B22, 39B52, 39A70 |
| url | https://arxiv.org/abs/2505.16323 |