和型积分算子在向量值函数逼近中的应用

Application of Sum-Integral Type Operators to Approximation of Vector-Valued Functions

给出一类和型及和型积分算子的构造法，对ｎ元向量值连续函数建立了这类算子的逼近定理，并给出了逼近的量化估计。特别，由所得的主要结果给出ｎ元 Ｃ０类算子半群的表示公式。

A method of constructing a class of sum-type and sum-integral type opera- tors is introduced. For n-dimensional vector-valued functions, approximation and relative estimation theorems of these operators are given. The author also uses the main results to construct representation formulas of the n-dimensional semi-groups of operators of (C0) class.