中文摘要：

研究某种特定形式的拟插值满足多项式再生性的充分必要条件。给出了几个定理,分别描述了常数再生、线性再生、二次多项式再生乃至一般的k次多项式再生的充分必要条件,并通过这些定理推出：LA不是常数再生的;LB是常数再生的但不是线性再生的;LD是线性再生的但不是二次多项式再生的。

英文摘要：

In this paper,the sufficient and necessary conditions are studied for a sort of quasi-interpolation when it is polynomial reproducing.Some theorems are given which describe the sufficient and necessary conditions as the quasi-interpolation is constant reproducing,linear reproducing,quadratic polynomial reproducing and the general polynomial reproducing of degree k respectively. From these theorems,LA isn t constant reproducing,LB is constant reproducing but not linear reproducing,and LD is linear reproducing but not quadratic polynomial reproducing.