The Schwarzian derivative and schlicht functions
The Schwarzian derivative and schlicht functions
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DOI：
10.1090/s0002-9904-1949-09241-8
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发表时间：
1949-06
影响因子：
1.3
通讯作者：
Z. Nehari
中科院分区：
文献类型：
--
作者：
Z. Nehari
单位圆内解析函数w-f(Z)，Schlicht的“Verzerrungssatz型”不等式通常是参照特定的规格化来表示的。(A)f(Z)在1上是有限的，/(O)=0，/‘(O)=1；(B)ƒ(Z)在2=0处有一个极点，剩余项为1。如果我们想得到与任何特定的规格化无关的不等式，我们必须使用关于z平面的任意线性变换不变的量。这类最简单的量是Schwarzian微分参数
It is customary to formulate the inequalities of the "Verzerrungssatz" type for analytic functions w—f(z), schlicht in the unit circle, with reference to a specific normalization. The two normalizations mainly used are: (a) f(z) is finite in \z\ < 1 , /(O) = 0 , /'(O) = 1; (b) ƒ(z) has a pole at 2 = 0 with the residue 1. If we want to obtain inequalities which are independent of any particular normalization, we have to use quantities which are invariant with regard to an arbitrary linear transformation of the z-plane. The simplest quantity of this type is the Schwarzian differential parameter