复指数系统在$L_{\alpha}^{p}$空间的不完备性

Incompleteness of Complex Exponential System in $L_{\alpha}^{p}$ Space

中文关键词:  不完备性  复指数系统  逼近论.

英文关键词:incompleteness  exponential system  approximation.

中文摘要:

      给出了复指数系统在加权Banach空间$L_{\alpha}^{p}=\{f:\int_{-\infty}^{ \infty}|f(t)e^{-\alpha(t)}|^{p}dt< \infty\}$上不完备的充要条件，其中$1\leq p< \infty$且$\alpha(t)$是定义在$\textbf{R}$上的权重.

英文摘要:

      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 $\textbf{R}$.