二元Marcinkiewicz型和的最佳逼近

The Optimal Approximation for Bivariate Marcinkiewicz Sum

首先研究了新的等距结点组上的二元连续周期函数的Marcinkiewicz型和的强性逼近问题,推广了一些文献中关于Marcinkiewicz型和的强性逼近的结论.进而又研究了该强性逼近的最佳逼近阶(饱和阶)的特征刻画,得到了该强性逼近的饱和阶的估计.此外,还研究并得到了该算子强性逼近连续周期函数的饱和类,从而彻底解决了一类等距结点组上的Marcinkiewicz型和的强性逼近问题及其相关的饱和问题.

In this paper,the optimal approximation for Marcinkiewicz sum is investigated by bivariate continuous and periodic functions.First,the strong approximation of Marcinkiewicz sum is arrived at a new equidistant and therefore some conclusions of strong approximation become a special case of the result in present paper.Then,the characteristics of estimate for optimal approximation order（saturation order） of strong approximation of Marcinkiewicz sum is considered.Moreover,the saturation class of strong approximation is confirmed.The problem of strong approximation of Marcinkiewicz sum of equidistant is solved and the problem of saturation problem is given completely.