单叶亚纯螺旋象函数的刻画和积分表示

Characterization and Integral Representation of Univalent Metamorphic Spirallike Functions

黎曼映射定理为复变函数的性质提供了几何刻画;Carathéodory收敛定理把函数像域的收敛与函数的收敛性紧密联系起来。利用黎曼映射定理、极值原理和Carathéodory收敛定理,研究极点在原点和极点在p点(0<p<1)的单叶亚纯螺旋象函数,得到了相应函数族的解析刻画和积分表示。

The Riemann mapping theorem provides a geometric characterization for the properties of complex functions;the Carathedory convergence theorem closely links the convergence of the function image field with the convergence of the function.Using the Riemann mapping theorem,the extreme value principle and the Carathedory convergence theorem,the univalent meromorphic spirallike functions with the pole at the origin and the pole at the p point(0<p<1)are studied,and the analytic characterization and integral representation of the corresponding function family are obtained.