| 复指数函数系的极小性 |
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| 引用本文： | 闫峰,邓冠铁.复指数函数系的极小性[J].数学研究及应用,2011,31(4):681-686. |
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| 作者姓名： | 闫峰 邓冠铁 |
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| 作者单位： | 邯郸学院数学系, 河北 邯郸 056005;北京师范大学数学科学学院, 北京 100875 |
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| 基金项目： | 国家自然科学基金(Grant No.10671022),高等学校博士点专项科研基金(Grant No.20060027023). |
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| 摘 要： | A sufficient condition is obtained for the minimality of the complex exponential system E（A, M） = {z^le^λnz： l = 0, 1,,.., mn - 1; n = 1, 2,...} in the Banaeh space La^p consisting of all functions f such that f^-a ∈ LP（N）. Moreover, if the incompleteness holds, each function in the closure of the linear span of exponential system E（A, M） can be extended to an analytic function represented by a Taylor-Dirichlet series.
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| 关 键 词： | minimality complex exponential system Taylor-Dirichlet series. |
| 收稿时间： | 2009/11/3 0:00:00 |
| 修稿时间： | 2010/4/27 0:00:00 |
Minimality of Complex Exponential System |
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| Feng YAN and Guan Tie DENG.Minimality of Complex Exponential System[J].Journal of Mathematical Research with Applications,2011,31(4):681-686. |
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| Authors: | Feng YAN and Guan Tie DENG |
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| Institution: | 1. Department of Mathematics, Handan College, Heibei, 056005, P.R.China
2. Schol of Mathematical Sciences and Key Laboratory of Mathematics and Complex System, Ministry of Education, Beijing Normal University, Beijing, 100875, P.R.China |
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| Abstract: | A sufficient condition is obtained for the minimality of the complex exponential system $E(\Lambda, M)=\{z^l e^{\lambda_n z}:l=0,1,\ldots,m_n-1;\ n=1,2,\ldots\}$ in the Banach space $L^p_\alpha$ consisting of all functions $f$ such that $f^{-\alpha}\in L^p({\mathbb{R}})$. Moreover, if the incompleteness holds, each function in the closure of the linear span of exponential system $E(\Lambda, M)$ can be extended to an analytic function represented by a Taylor-Dirichlet series. |
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| Keywords: | minimality complex exponential system Taylor-Dirichlet series |
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