圆盘自同构迭代的零点序列与Blaschke乘积

考虑单位圆盘上解析自同构零点的性质, 通过计算证明: 解析自同构中双曲型的和抛物型的在迭代后得到的零点所生成的Blaschke乘积具有插值性和单分支性, 椭圆型的在迭代后得到的零点不趋于边界, 不能生成Blaschke乘积.

Zero Sequence of Automorphism Iteration in Disk with Blaschke Product

We considered the properties of zeros of analytic automorphisms on the unit disk. It is proved by calculation that the Blaschke product generated by the zeros of hyperbolic and parabolic analytic automorphism after iteration has the properties of interpolation and one-component, and the zeros of elliptic analytic automorphism after iteration does not tend to the boundary, so it can not generate Blaschke product.