Incompleteness and Minimality of Exponential System  

作　　者：Si Yu KE Guan Tie DENG 

机构地区：[1]School of Mathematical Sciences and Key Laboratory of Mathematics and Complex System, Ministry of Education, Bcijing Normal University, Beijing 100875, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2011年第2期215-223,共9页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 11071020);the Research Foundation for Doctor Program (Grant No. 20100003110004)

摘　　要：Necessary and sufficient conditions are obtained for the incompleteness and the minimality of the exponential system E（Λ,M） = {z l e λ n z ： l = 0,1,...,m n-1;n = 1,2,...} in the Banach space E 2 [σ] consisting of some analytic functions in a half strip.If the incompleteness holds,each function in the closure of the linear span of exponential system E（Λ,M） can be extended to an analytic function represented by a Taylor-Dirichlet series.Moreover,by the conformal mapping ζ = φ（z） = e z ,the similar results hold for the incompleteness and the minimality of the power function system F （Λ,M） = {（log ζ） l ζ λ n ： l = 0,1,...,m n-1;n = 1,2,...} in the Banach space F 2 [σ] consisting of some analytic functions in a sector.Necessary and sufficient conditions are obtained for the incompleteness and the minimality of the exponential system E（Λ,M） = {z l e λ n z ： l = 0,1,...,m n-1;n = 1,2,...} in the Banach space E 2 [σ] consisting of some analytic functions in a half strip.If the incompleteness holds,each function in the closure of the linear span of exponential system E（Λ,M） can be extended to an analytic function represented by a Taylor-Dirichlet series.Moreover,by the conformal mapping ζ = φ（z） = e z ,the similar results hold for the incompleteness and the minimality of the power function system F （Λ,M） = {（log ζ） l ζ λ n ： l = 0,1,...,m n-1;n = 1,2,...} in the Banach space F 2 [σ] consisting of some analytic functions in a sector.

关 键 词：INCOMPLETENESS MINIMALITY exponential system 

分 类 号：O174.5[理学—数学] O174.52[理学—基础数学]