部分和有界的级数在Cesaro意义下收敛性的条件

Convergence Condition of Series with Finite Partial Sums under Cesaro

将级数在Cesaro意义下的收敛性转化为适当数列的均值收敛问题,巧妙构造一个有界数列得到了有界数列均值收敛性的一般性结论,再通过建立数列的有限权重分解,得到了关于有界数列均值收敛的一些有益的结论,进而更完整地解决了级数在Cesaro意义下收敛性的条件问题.

In this paper,we change the series convergence under Cesaro into the mean convergence of a appropriate sequence of number.Through constructing a bounded sequence of number skillfully,we get the general conclusion of the mean convergence of bounded sequence of number.Furthermore,we give the finite weight decomposition of sequence of number by introducing the weight of subsequence,and derive some useful results about the mean convergence of bounded sequence of number.With all above discussions,we resolve the series convergence under Cesaro completely.