半平面中解析函数的积分表示及在逼近中的应用  

Integral Representation of Functions Analytic in the Right Half Plane and Applications in Approximation

作　　者：杨向东[1] 邓冠铁[2] 

机构地区：[1]昆明理工大学数学系,昆明650093 [2]北京师范大学数学科学学院数学与复杂系统教育部重点实验室,北京100875

出　　处：《数学物理学报（A辑）》2008年第6期1242-1250,共9页Acta Mathematica Scientia

基　　金：昆明理工大学人才引进项目(14118029)资助

摘　　要：在该文中,作者证明了满足一定增长性条件的右半平面上的解析函数可以由它在边界上的积分和其加权Blaschke乘积的和表示,作为应用,作者还考虑了指数多项式在实数轴上加权Banach空间C_α中的完备性.In this paper, we prove that analytic functions in the right halt plane with some restricted growth can be represented by a sum of its weighted Blaschke product and its integral on the boundary of the half plane. As its applications, we also investigate the completeness of complex exponential polynomials in Cα, where Cα is a weighted Banach space of complex continuous functions f on the real axis R with f（t）exp（-α（t）） vanishing at infinity, in the uniform norm with respect to the weight α（t）.

关 键 词：解析函数 Blaschke乘积 积分表示 完备性 

分 类 号：O174.52[理学—数学]