| 复指数系统在$L_{\alpha}^{p}$空间的不完备性 |
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| 引用本文： | 范协铨,邓冠铁.复指数系统在$L_{\alpha}^{p}$空间的不完备性[J].数学研究及应用,2010,30(6):1078-1082. |
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| 作者姓名： | 范协铨 邓冠铁 |
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| 作者单位： | 北京师范大学数学科学学院, 数学与复杂系统教育部重点实验室, 北京 100875;北京师范大学数学科学学院, 数学与复杂系统教育部重点实验室, 北京 100875 |
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| 基金项目： | 国家自然科学基金(Grant No.10671022),高等学校博士点基金(Grant No.20060027023). |
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| 摘 要： | A necessary and sufficient condition is obtained for the incompleteness of complex exponential system in the weighted Banach space Lαp = {f：∫＋∞∞ ｜f（t）e-α（t）｜pdt ＋∞},where 1 ≤ p ＋∞ and α（t） is a weight on R.
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| 关 键 词： | incompleteness exponential system approximation. |
| 收稿时间： | 2008/10/22 0:00:00 |
| 修稿时间： | 2009/9/15 0:00:00 |
Incompleteness of Complex Exponential System in $L_{\alpha}^{p}$ Space |
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| Xie Quan FAN and Guan Tie DENG.Incompleteness of Complex Exponential System in $L_{\alpha}^{p}$ Space[J].Journal of Mathematical Research with Applications,2010,30(6):1078-1082. |
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| Authors: | Xie Quan FAN and Guan Tie DENG |
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| Institution: | Key Laboratory of Mathematics and Complex Systems, Ministry of Education, China, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China;Key Laboratory of Mathematics and Complex Systems, Ministry of Education, China, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China |
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| Abstract: | A necessary and sufficient condition is obtained for the incompleteness of complex exponential system in the weighted Banach space $L_{\alpha}^{p}=\{f:\int_{-\infty}^{+\infty}|f(t)e^{-\alpha(t)}|^{p}\d t<+\infty\}$, where $1\leq p<+\infty$ and $\alpha(t)$ is a weight on $\textbf{R}$. |
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| Keywords: | incompleteness exponential system approximation |
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