关于Grünwald算子的多元推广

On the multivariate generalization of the Grünwald operator.

考虑 R2 中三角域和多边形域上的 Grünwald插值算子及其一种基于非负凸组合的有理变形 ,证明了两种插值的存在性和唯一性 ,给出了相应的逼近估计 ,且最后的逼近估计是精确的 ,从而给出了Grünwald算子非乘积型多元推广不分片和分片的两个范例。

The Grünwald interpolation operator and it's variant in the region of a trigon and polygon of R\+2 and a rational variant based on nonnegative convex combination are considered. The exsistence and uniqueness of two interpolation are proved, the estimation of error of approximation is exact. Therefore the two example of Grünwald operator's multivariate generalization of nonmultiplicative on nonpartitioning and partition are given.