| 广义函数Denjoy积分的收敛性问题 |
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| 引用本文： | 刘巧玲,叶国菊.广义函数Denjoy积分的收敛性问题[J].数学学报,2011(4):659-664. |
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| 作者姓名： | 刘巧玲 叶国菊 |
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| 作者单位： | 河海大学理学院; |
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| 基金项目： | 国家自然科学基金资助项目(10871059) |
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| 摘 要： | 本文讨论广义函数De njoy积分的收敛性问题.首先给出了广义Denjoy可积函数空间中强收敛、弱收敛、弱~*收敛和广义函数Denjoy积分收敛的关系;证明拟一致收敛是广义函数Denjoy积分收敛的一个充分必要条件;最后指出了Denjoy可积广义函数列弱~*收敛与强收敛等价当且仅当原函数等度连续.
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| 关 键 词： | 广义函数Denjoy积分 强收敛 弱收敛 |
Some Problems on the Convergence of Distributional Denjoy Integral |
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| Qiao Ling LIU Guo Ju YE College of Science,Hohai University,Nanjing ,P.R.China.Some Problems on the Convergence of Distributional Denjoy Integral[J].Acta Mathematica Sinica,2011(4):659-664. |
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| Authors: | Qiao Ling LIU Guo Ju YE College of Science Hohai University Nanjing PRChina |
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| Institution: | Qiao Ling LIU Guo Ju YE College of Science,Hohai University,Nanjing 210098,P.R.China |
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| Abstract: | This paper discusses some problems on the convergence of distributional Denjoy integral.Firstly,we give the relations between strong convergence,weak convergence, weak* convergence and distributional Denjoy integral convergence in the space of Denjoy integrable distributions.We prove the quasi-uniform convergence is a sufficient and necessary condition of the convergence of distributional Denjoy integral.Finally, we show that weak* convergence and strong convergence are equivalent if and only if the sequenc... |
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| Keywords: | Denjoy distributional integral strong convergence weak convergence |
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