关于勃拉希克型逼近的注记（英文）  

A note on Blaschke-type approximation

作　　者：赵晓辉[1,2] 杨广武[1] 

机构地区：[1]河北科技大学理学院,石家庄050018 [2]河北工程技术学院经济管理学院,石家庄050091

出　　处：《黑龙江大学自然科学学报》2016年第2期200-204,共5页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Scientific Research Project of Hebei Provincial Department of Education(2350044)

摘　　要：研究关于哈代空间中复平面内单位圆盘上解析函数的勃拉希克型逼近。在一定条件下,标准化的勃拉希克乘积B_1(z),B_2(z),…构成单位圆盘上哈代空间的Takenaka-Malmquist(TM)正交系,一个解析函数f在该正交系下展开式的n次系数由c_n=<f,B_n>给定。在Qian(2013年)的文献中,c_n依靠一个循环公式来计算。利用共轭原理和残数定理,给出c_n一个显式表达,纠正了Soumelidis(2002年)文献中公式的错误。基于新的公式,给出Takenaka-Malmquist正交系完备性的一个简化证明,并导出几个有趣的恒等式。Consider the Blaschke-type approximation of analytic functions in Hardy space defined on the unit disk of the complex plane. It is known that under a certain condition the normalized Blaschke prod- ucts BI（Z）, B2 （z）, …… form an orthogonal basis for the Hardy space, which is called the Takenaka-Malmquist system. Then, the n-the coefficient in the orthogonal system of an analytic function f is cn =〈f, Bn 〉. In the literature of Qian 2013, cn is computed by a recurrence formula. By applying the con- jugate principle and the residue theorem, an explicit formula for the coefficient cn is obtained, which cor- rects the wrong formula in Soumelidis 2002. From which, a simpler proof for the completeness of the Tak- enaka-Malmquist orthogonal system is given and several interesting identities are obtained.

关 键 词：有理逼近 勃拉希克乘积 塔克那卡-马勒亏斯特标准正交系 哈代空间 

分 类 号：O189.1[理学—数学]