| 均值有界变差条件及其在Fourier分析中的应用 |
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| 引用本文： | 周颂平,ZHOU Ping,虞旦盛.均值有界变差条件及其在Fourier分析中的应用[J].数学研究及应用,2008,28(4):753-758. |
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| 作者姓名： | 周颂平 ZHOU Ping 虞旦盛 |
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| 作者单位： | 浙江理工大学数学所, 浙江 杭州 310028;Department of Mathematics, Statistics and Computer Science, St. Francis University, Antigonish Nova Scotia Canada, B2G 2W5;浙江理工大学数学所, 浙江 杭州 310028 |
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| 基金项目： | Open Funds of State Key Laboratory of Oil and Gas Reservoir and Exploitation of Southwest Petroleum University (No.PCN0613); NSERC of Canada; the NSERC RCD grant and AARMS of Cananda. |
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| 摘 要： | 本文宣布了关于Fourier (三角)级数的系数数列单调性条件的一个最终推广.我们已经证明了该条件对正弦级数保持一致收敛性方面已不可作任何推广,一些Fourier分析中重要和有趣的经典定理也已经在此最终条件下重新建立.本文因而对长达90年的研究历史作了一个简要综述.这一系列论文中的第一篇原始论文公布在arXiv:math.CA/0611805 v1, November 27, 2006.
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| 关 键 词： | 均值有界变差数列 三角级数 收敛 可积性 最佳逼近. |
| 收稿时间： | 2006/12/22 0:00:00 |
| 修稿时间： | 2007/3/26 0:00:00 |
Mean Bounded Variation Condition and Applications in Fourier Analysis |
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| ZHOU Song Ping,ZHOU Ping and YU Dan Sheng.Mean Bounded Variation Condition and Applications in Fourier Analysis[J].Journal of Mathematical Research with Applications,2008,28(4):753-758. |
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| Authors: | ZHOU Song Ping ZHOU Ping and YU Dan Sheng |
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| Institution: | Institute of Mathematics, Zhejiang Sci-Tech University, Zhejiang 310018, China;Department of Mathematics, Statistics and Computer Science, St. Francis University, Antigonish Nova Scotia Canada, B2G 2W5;Department of Mathematics, Statistics and Computer Science, St. Francis University, Antigonish Nova Scotia Canada, B2G 2W5 |
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| Abstract: | This announcement is to raise an ultimate generalization to monotonicity condition on the Fourier (trigonometric) coefficient sequences. We prove this condition cannot be weakened any further to guarantee the uniform convergence of the sine series. Some interesting and important classical results in Fourier analysis are re-established under this ultimate condition. Over ninty year research history is surveyed in this announcement.The first original paper of this series of papers is posted in arXiv:math.CA/0611805 v1, November 27, 2006. |
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| Keywords: | MVBVS trigonometric series convergence integrability best approximation |
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