向量函数级数一致收敛性的判定

Determination of Uniform Convergence of Vector Function Series

对比函数项级数,给出了向量函数级数的概念,并通过研究函数项级数的一致收敛性,得到与函数项级数类似的向量函数级数一致收敛的判定方法,即Cauchy准则、魏尔斯特拉斯判别法、根式判别法、余项准则,完善了向量函数的级数理论。在文章最后给出向量函数级数的简单性质。

Through analog Series of functional terms,this paper gives the concept of vector function series and the judgment method of uniform convergence of vector function series is obtained.The identification method of uniform convergence including Cauchy criterion,Wellstrass,Radical test,Complementary criteria,the series theory of vector function is improved.At the end of the paper,the simple properties of the series of vector functions are given.