| Completeness of Complex Exponential System in $L^p_\alpha$ Space |
| Received:June 21, 2006 Revised:December 12, 2006 |
| Key Words:
completeness complex exponential system approximation.
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| Fund Project:the National Natural Science Foundation of China (No.10671022); the Research Fund for the Doctoral Program of Higher Education (No.20060027023). |
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| Abstract: |
| A necessary and sufficient condition is obtained for the complex exponential system to be dense in the weighted Banach space $L_{\alpha}^p=\{f:\int_{-{\infty}}^{\infty}|f(t)e^{-\alpha(t)}|^p\mathrm{d}t <{\infty}\}$, where $1\le{p}<+{\infty}$ and $\alpha(t)$ is a nonnegative continuous function on $\bf R$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.03.032 |
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