【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B₁（z）,B₂（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。更多还原

【Abstract】 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 products B₁（z）,B₂（z）,… form an orthogonal basis for the Hardy space,which is called the TakenakaMalmquist system.Then,the n-the coefficient in the orthogonal system of an analytic function f is c_n=< f,B_n>.In the literature of Qian 2013,c_n is computed by a recurrence formula.By applying the conjugate principle and the residue theorem,an explicit formula for the coefficient cnis obtained,which corrects the wrong formula in Soumelidis 2002.From which,a simpler proof for the completeness of the Takenaka-Malmquist orthogonal system is given and several interesting identities are obtained.更多还原