The Analytic Fixed Point Function in the Disk

被引：0
|
作者：
Diego Mejía
Christian Pommerenke
机构：
[1] Universidad Nacional,Departamento de Matemáticas
[2] Technische Universität,Institut für Mathematik, MA 8–2
来源：
Computational Methods and Function Theory | 2006年 / 5卷 / 2期
关键词：
Fixed point function; byperbolically convex; coefficients; asymptotic behaviour; probability generating function; large deviations; branching process; 30D50; 30D05; 60F10;
D O I：
10.1007/BF03321099
中图分类号：
学科分类号：
摘要：
Let φ be analytic in the unit disk D and let φ(D) ⊂ D, φ(0) ≠ 0. Then ω = z/φ(z) has an analytic inverse z = f(ω), ω ∈ D, the fixed point function. Here f(D) is a starlike domain and various results suggest that f(D) might even be hyperbolically convex. We study the derivative and the coefficients of f, in particular their asymptotic behaviour. In the case that φ is the generating function of a random variable, several functions related to f have probabilistic interpretations.
引用
收藏
页码：275 / 299
页数：24
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