一元三角插值序列的线性求和问题

On a linear summation problem of trigonometric interpolation sequences of one component

通过对Fourier部分和做适当的构造,可得到一致收敛的求和算子,而求和因子法是一种行之有效的方法被广泛使用.但是一般文献中利用的求和因子法构造的算子在使用上具有很强的约束性.基于求和因子法和Fourier级数与等距结点上的三角插值多项式的相似性,对一些不能一致收敛的一元三角插值算子进行新的相关构造,得出一类一致收敛的一元Fourier部分和算子和离散的一元Fourier部分和算子,给出了它们收敛阶的估计,得到该类算子的饱和阶.并且推广了一些文献中的结论,并且本文给出的方法更具有一般性.

As we know, an uniform convergence operator is constructed through Fourier sums. The summation factor was widely used and applied in many areas, but its application was limited in many aspects. In this paper, the problem considered here is changed to a kind of trigonometric interpolation sequences, which is similar to Fourier series of trigonometric interpolation on an equidistant node set. Therefore the operator sequences of the Fourier sum and the discrete Fourier sum could be converged uniformly. Their convergence order is estimated to oblain the saturation order of them. The method of the present paper can be used extensively.