指数多项式在半带形中的闭包

数学物理学报

指数多项式在半带形中的闭包

邓冠铁

北京师范大学数学科学学院, 北京 100875

收稿日期:2005-07-10 修回日期:2006-06-23 出版日期:2007-06-25 发布日期:2007-06-25
通讯作者: 邓冠铁
基金资助:
国家自然科学基金(10371011、10071005)和教育部留学回国人员科研启动基金资助

Closure of Exponential Polynomials in a Half Strip

Deng Guantie

Schoole of Mathematical Sciences, Beijing Normal University, Beijing 100875

Received:2005-07-10 Revised:2006-06-23 Online:2007-06-25 Published:2007-06-25
Contact: Deng Guantie

摘要/Abstract

摘要： 该文对一类复指数多项式组成的线性空间$M(\Lambda )$ 在Banach 空间 H_α中的不完备性给出了充分必要条件, 其中 H_α为在半带形 I_α={z=x+iy: x≥ 0, |y|≤α} (α > 0 )中连续, 在I_α的内部解析且当 x→∞时, f(x+ iy)在I_α中关于 y 一致地趋向 0 的函数 f(x+ iy)全体, 其范数为上确界范数. 同时指出, 如果$M(\Lambda )$ 在 H_α中不完备, 则它的闭包cl$(M(\Lambda ))$中所有的函数都可以延拓为由Dirichlet级数表示的解析函数.

关键词: 指数多项式, 不完备性, 闭包

Abstract: In this paper, the author obtains a necessary and sufficient condition
for the incompleteness of complex exponential polynomials in the Banach space H_α consisting of all continuous functions f on the closed right half strip I_α={z=x+iy: x≥ 0, |y|≤α} (α > 0 ), analytic in its interior and such that f(z) vanishing uniformly at infinity. The author also proves that, if some conditions of incompleteness hold, then each function in the closure of the set of complex exponential polynomials can be extended to an analytic function represented by a Dirichlet series.

Key words: Incompleteness, Closure, Exponential polynomials

中图分类号:

30B50

邓冠铁. 指数多项式在半带形中的闭包[J]. 数学物理学报, 2007, 27(3): 414-419.

Deng Guantie. Closure of Exponential Polynomials in a Half Strip[J]. Acta mathematica scientia,Series A, 2007, 27(3): 414-419.

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