| 一种求和法及其应用 |
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| 引用本文： | 王佛生,吴定平,谢旭平.一种求和法及其应用[J].成都信息工程学院学报,2011,26(1):57-60. |
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| 作者姓名： | 王佛生 吴定平 谢旭平 |
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| 作者单位： | 成都信息工程学院数学学院; |
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| 摘 要： | 为了用泛函的方法解决收敛问题,通过应用拓扑向量空间的一些性质,将一个序列到另一个序列的变化看作是变换,得到复距离空间中一些序列收敛性的等价条件.改进和推广了Abel定理,Mertens定理,O.Stolze公式等.
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| 关 键 词： | 泛函分析 拓扑向量空间 求和法 复序列 Banach-Steinhaus定理 Abel定理 Stolze公式 |
A Summation Method and Its Application |
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| WANG Fu-sheng,WU Ding-ping,XIE Xu-ping.A Summation Method and Its Application[J].Journal of Chengdu University of Information Technology,2011,26(1):57-60. |
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| Authors: | WANG Fu-sheng WU Ding-ping XIE Xu-ping |
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| Institution: | WANG Fu-sheng,WU Ding-ping,XIE Xu-ping(School of Mathematics,CUIT,Chengdu 610225,China) |
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| Abstract: | In order to solve convergence problems in a functional way,some properties of topological vector spaces are used to view the changes of one sequence to another as a linear transformation.Some equivalent conditions of convergence of sequences in complex metric spaces are obtained as well.The Abel Theorem, Mertens Theorem and O.Stolze Formula have been improved and generalized. |
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| Keywords: | functional analysis topological vector space summation methods complex sequences Banach-Seinhaus theorem Abel theorem Stolze formula |
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