| Incompleteness of Complex Exponential System in $L_{\alpha}^{p}$ Space |
| Received:October 22, 2008 Revised:September 15, 2009 |
| Key Words:
incompleteness exponential system approximation.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10671022) and the Research Fund for the Doctoral of Higher Education (Grant No.20060027023). |
| Author Name | Affiliation | | Xie Quan FAN | Key Laboratory of Mathematics and Complex Systems, Ministry of Education, China, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China | | Guan Tie DENG | 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 $\textbf{R}$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.06.017 |
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