On the polynomiality of different polynomial functions in many variables

Kosovan Vasyl Mykhailovych

Kosovan Vasyl Mykhailovych ¹

¹ Department of Mathematical Modeling, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

Keywords: the polynomialit, different polynomial functions

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Abstract

We prove theorems on the joint polynomiality of separately polynomial functions of several variables. In particular, we obtain a general representation of separately polynomial mappings $f: X_1 × ... × X_n → K,$ де $X_k$ for the case where every $X_k$ is a subset of a field $K,f$ is polynom of a fixed power $m_k$ with respect to each variable $x_k$ and $|X_k| > m_k$ for all $k$ except for at most one.

References

[1] Kosovan V.M., Maslyuchenko V.K. Variously polynomial functions // Scientific Bulletin of Chernivtsi University. В. 374 . Mathematics. - 2008. - P. 66-74.

[2] Kosovan V.M., Maslyuchenko V.K. Differentially and cumulatively polynomial functions on arbitrary sets $\mathbb{R}^n$ // Scientific Bulletin of Chernivtsi University. В. 454 . Mathematics. - 2009. - p. 50-53.

[3] Kosovan V.M., Maslyuchenko V.K. On (m,n)-polynomial functions on products and non-negatively polynomial functions on crosses // Nauk. Visnyk of Chernivtsi Univ. Seriya: Mat. 2-3(3) , - 2012. - P.108-113.

[4] Mazur S., Orlich W. Grundlegende Eigenshaften der polynomischen Operationen // Studia Math. − 1935. − 5 − S.50-68.

[5] Kosovan V.M., Maslyuchenko V.K. On the polynomiality of non-parametric functions // Mathematical Bulletin of the National Technical School - 2008 - 5 - P.89-96.

[6] Kurosh A.G. Course of higher algebra.- M.: Nauka, 1971.- 432 p.

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Cite

ACS Style: Kosovan, V.M. On the polynomiality of different polynomial functions in many variables. Bukovinian Mathematical Journal. 2016, 2
AMA Style: Kosovan VM. On the polynomiality of different polynomial functions in many variables. Bukovinian Mathematical Journal. 2016; 2(2-3).
Chicago/Turabian Style: Vasyl Mykhailovych Kosovan. 2016. "On the polynomiality of different polynomial functions in many variables". Bukovinian Mathematical Journal. 2 no. 2-3.

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