几个三角求和算子的线性组合

Linear Combination of Several Operators of Triangle Summation

通过对已有几个三角求和算子进行线性组合,构造一个新算子Tn(f;x).证明该算子在全实轴上一致收敛于任意以2π为周期的连续函数f(x),得到了当f(x)∈Cj2π(0≤j≤7)时算子的最佳收敛阶,并且证明了算子的最高收敛阶不会超过1/n8.在收敛性方面,所构造的新算子明显优于其他算子.

A new triangle summation operator, T_n(f;x), is constructed via linearly combining several known operators. It is proved that this operator converges to arbitrary continuous function f(x) with period 2π on the whole axis. If f(x)C^j_(2π)(0j7), the best convergence order of the operator is obtained. Finally, it is proved that the highest convergence order of the operator does not exceed 1/n^8. The new operator constructed in this paper is superior to other operators in convergency.