对于单位圆盘Δ内的单叶函数f,利用其Schwarzian导数的高阶导数对Aharonov不变量进行刻画,得到了 Aharonov 不变量的一个显式表达式.引入 Lavie 导数,建立了它与函数 f 的Schwarzian导数的高阶导数以及Aharonov不变量之间的关系,并对Lavie导数的模作一个简单的刻画.
A Note on the Aharonov Invariants
For a univalent function f in the unit disk Δ,the Aharonov invariants are characterized by the higher-order derivative of its Schwarzian derivative,and a explicit formula of the Aharonov invariants is obtained.By introducing the Lavie derivative,establishes its relationship with the higher-order derivatives of the Schwarzian derivative offand the Aharonov invariants,and gives a simple characterization of the modulus of Lavie derivative.
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