Examples of separately polynomial functions defined on subsets of $\mathbb{R}^2$ which are not jointly polynomial are given. A general theorem on the polynomiality of a separately polynomial function $f: E → \mathbb{R}$ where $E ⊆ \mathbb{R}^n,$ which is usable when $E$ is a domain in $\mathbb{R}^n$ is established.
[1] Bochnak J., Siciak J. Polynomials and multilinear mappings in topological vector spaces // Stud. Math. - 1971. - 39 . - P. 59-76.
[2] Kosovan V.M., Maslyuchenko V.K. Differently polynomial functions // Scientific bulletin of Chernivtsi University. Issue 374. Mathematics. - Chernivtsi: Ruta, 2008. - P. 66-74.
[3] Kosovan V.M., Maslyuchenko V.K. Differently polynomial functions on arbitrary subsets of $\mathbb{R}^n$ // IV All-Ukrainian scientific conference "Nonlinear problems of analysis" (September 10-12, 2008, Ivano-Frankivsk). Abstracts of reports. - Ivano-Frankivsk, 2008. - P. 51.
- ACS Style
- Kosovan, V.M.; Maslyuchenko, V.K. Separately and jointly polynomial functions on arbitrary subsets $\mathbb{R}^n$. Bukovinian Mathematical Journal. 2018, 1
- AMA Style
- Kosovan VM, Maslyuchenko VK. Separately and jointly polynomial functions on arbitrary subsets $\mathbb{R}^n$. Bukovinian Mathematical Journal. 2018; 1(454).
- Chicago/Turabian Style
- Vasyl Mykhailovych Kosovan, Volodymyr Kyrylovych Maslyuchenko. 2018. "Separately and jointly polynomial functions on arbitrary subsets $\mathbb{R}^n$". Bukovinian Mathematical Journal. 1 no. 454.