Inverse problem for zeros of certain koebe-related functions

Abstract

If w₁,…,w _N is a finite sequence of nonzero points in the unit disk, then there are distinct points λ₁,…, λ_N on the unit circle and positive numbers Μ₁,…,Μ _N such that$w_1 ,...,w_N , 1/\bar w_1 ,...1/\bar w_N$ is the zero sequence of the function 1 —$\sum\nolimits_{l = 1}^N {\left[ {\mu _1 \bar \lambda _1 z/\left( {1 - \bar \lambda _1 z} \right)^2 } \right]}$. The points λ₁,…, λ_N and numbers Μ₁,…,Μ_N are unique (except for reorderings).