Incompleteness of Complex Exponential System in $L_{\alpha}^{p}$ Space
Received:October 22, 2008  Revised:September 15, 2009
Key Words: incompleteness   exponential system   approximation.  
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 NameAffiliation
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 
Hits: 2547
Download times: 1993
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
View Full Text  View/Add Comment