多项式空间的对偶及其在多元插值中的应用

本文通过把域Ｋ上ｎ元多项式环看成域Ｋ上的无限维向量空间Ａ，把ｎ维仿射空间Ｋ＾ｎ中的每一点看成Ａ上的线性泛函，从而Ｋ＾ｎ为对偶空间Ａ＾＊的子集，利用对偶空间的理论得到了一些有趣的理论结果，弄清了Ｋ＾ｎ上点有限拓扑的结构，给出了判定给定结点组是否是给定多项式空间的适定结点组的判定准则，最后还给出了构造理想对偶基的一种算法。

The Dual Space of Polynomials and Its Application on Interpolation in Several Variables

This paper presents some interest results by regarding polynomial ring as an infinite dimensional vector space A over the coefficient field and n dimensional affine space K n as a subspace of the dual space A * of vector sapace A. It clarifies the construction of the point finite topology over K n. Based on these results, a criterion is given, which can detect whether a set of segment points is properly posed for preassigned polynomial space. In the end, an algorithm to construct a dual basis of an ideal is put forward.