| 随机Dirichlet级数在L2中的收敛性 |
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| 引用本文： | 王志刚,田范基.随机Dirichlet级数在L2中的收敛性[J].河北大学学报(自然科学版),2011,31(6):561-566. |
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| 作者姓名： | 王志刚 田范基 |
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| 作者单位： | 1. 海南大学数学系,海南海口,570228
2. 湖北大学数学与计算机科学学院,湖北武汉,430062 |
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| 基金项目： | 海南省教育厅高等学校科学研究资助项目(Hjkj200908); 湖南大学教育教学研究资助课题(hdjy1102) |
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| 摘 要： | 利用对称化方法,获得了独立序列在满足正则性条件下,随机Dirichlet级数在L2中收敛与a.s.收敛的等价性.将随机Dirichlet级数a.s.收敛性转化为某Dirichlet级数的收敛性,得到新的Valiron公式和Knopp-Bohr公式和收敛横坐标的简洁公式.
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| 关 键 词： | 随机Dirichlet级数 收敛横坐标 Lr收敛 方差 |
Convergence of Random Dirichlet Series in L_2 |
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| WANG Zhi-gang,TIAN Fan-ji.Convergence of Random Dirichlet Series in L_2[J].Journal of Hebei University (Natural Science Edition),2011,31(6):561-566. |
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| Authors: | WANG Zhi-gang TIAN Fan-ji |
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| Institution: | WANG Zhi-gang1,TIAN Fan-ji2(1.Department of Mathematics,Hainan University,Haikou 570228,China,2.Institute of Mathematics and Computer Science,Hubei University,Wuhan 430062,China) |
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| Abstract: | By the method of symmetrization,the authors study that the equivalence between the convergence in L2 and almost sure convergence of random Dirichlet series under some conditions.After analyzing the results,obtain that the convergence of random Dirichlet series is transformed into the convergence of some Dirichlet series.Valiron and Knopp-Bohr formulae in new forms and some interesting results are obtained. |
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| Keywords: | rondom dirichlet series abscissa of convergence convergence in Lr variance |
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