| 随机级数的自然边界 |
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| 引用本文： | 卢方芳.随机级数的自然边界[J].湖北大学学报(自然科学版),2006,28(1):12-14. |
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| 作者姓名： | 卢方芳 |
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| 作者单位： | 湖北大学数学与计算机科学学院,湖北武汉430062 |
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| 摘 要： | 利用一个有关解析函数项级数S-可和的引理,以及对称随机级数的S-和及a.s.收敛性关系,有下列结果:一般对称随机解析函数项级数的收敛边界几乎必然是自然边界.特别地,对称随机Taylor级数,随机Dirichlet级数,随机罗朗级数等的收敛边界几乎必然是自然边界.
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| 关 键 词： | S-可和 a.s.收敛 自然边界 对称随机级数 |
| 文章编号： | 1000-2375(2006)01-0012-03 |
| 收稿时间： | 12 17 2004 12:00AM |
| 修稿时间： | 2004年12月17 |
The natural boundary of random series |
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| LU Fang-fang.The natural boundary of random series[J].Journal of Hubei University(Natural Science Edition),2006,28(1):12-14. |
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| Authors: | LU Fang-fang |
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| Institution: | School of Mathematics and Computer Science, Hubei University, Wuhan 430062, China |
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| Abstract: | By use an important lemma on the S - summability of analytic series, and the S a.s. convergenec of symmetric random series. More that the boundary of convergence of general - summability and symmetric random analytic series is a natural boundary. Especially, for symmetric random Taylor series, random Diriehlet series, random Laurent series and so on, the boundaries of convergence of these series are natural boundaries. |
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| Keywords: | S - sums almost surely convergence natural boundary symmetric random series |
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