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.  
Fund Project:the National Natural Science Foundation of China (No.10671022); the Research Fund for the Doctoral Program of Higher Education (No.20060027023).
Author NameAffiliation
Yan Feng Sch. Math. Sci. \& Lab. Math. Com. Sys., Beijing Normal University, Beijing 100875, China
Department of Mathematics, Handan College, Hebei 056004, China 
DENG Guan Tie Sch. Math. Sci. \& Lab. Math. Com. Sys., Beijing Normal University, Beijing 100875, China 
Hits: 2873
Download times: 1848
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
View Full Text  View/Add Comment