论文标题
在偏斜的部分衍生物和Hermite型插值问题上
On skew partial derivatives and a Hermite-type interpolation problem
论文作者
论文摘要
令$ \ mathcal {r}：= \ mathbb {f} [{\ bf x};σ，δ] $是一个多元偏度多项式环，上面是分区环$ \ mathbb {f} $。在本文中，我们介绍了左右$（σ，δ）$的概念 - $ \ Mathcal {r} $中多项式的部分衍生物，我们证明了它们的一些主要属性。作为这些结果的应用，我们解决了$ \ Mathcal {r} $ a hermite-type多元偏斜多项式插值问题。这里使用的主要技术工具和结果是建设性类型，显示了在$ \ Mathcal {r} $中构造多项式的方法和算法，该{R} $满足了上述Hermite型插值问题及其相对Lagrange-type版本。
Let $\mathcal{R}:=\mathbb{F}[{\bf x};σ,δ]$ be a multivariate skew polynomial ring over a division ring $\mathbb{F}$. In this paper, we introduce the notion of right and left $(σ,δ)$-partial derivatives of polynomials in $\mathcal{R}$ and we prove some of their main properties. As an application of these results, we solve in $\mathcal{R}$ a Hermite-type multivariate skew polynomial interpolation problem. The main technical tools and results used here are of constructive type, showing methods and algorithms to construct a polynomial in $\mathcal{R}$ which satisfies the above Hermite-type interpolation problem and its relative Lagrange-type version.
