关于上密度无限制的缺项多项式加权逼近(英文)  

On Weighted Polynomial Approximation with Unrestricted Upper Density Gaps

作　　者：杨向东[1] 

机构地区：[1]昆明理工大学数学系,云南昆明650093

出　　处：《应用数学》2010年第3期665-669,共5页Mathematica Applicata

基　　金：Supported by YunNan Provincial Basic Research Foundation (2009ZC013X);Basic Research Foundation of Education Bureau of YunNan Province (09Y0079)

摘　　要：令Cα为由在实轴R上连续且满足f(t)exp(-α(t))→0的函数f组成的Banach空间,其中α(t)为非负连续函数.在本文中,我们得到缺项的多项式在Cα中不完备的充分条件.本文的要点在于我们不要求上密度是有限的.Let Cα be the weighted Banach space of complex continuous functions f defined on the real axis R with f（t）exp（-α（t）） vanishing at infinity in the uniform norm,where α（t） is a nonnegative continuous function.In this paper,we obtain sufficient condition for polynomial with gaps not to be dense in Cα.The point here in our paper is that the gaps are not required to have a finite upper density.

关 键 词：多项式逼近 BANACH空间 上密度 

分 类 号：O174.5[理学—数学]