The Boundary Behavior of Holomorphic Functions

In the theory of several complex variables, the Fatou type problems, the Lindel\"{o}f principle, and inner functions have been well studied for strongly pseudoconvex domains. In this thesis, we are going to study more generalized domains, those of finite type. In Chapter 2 we show that there is no Fatou's theorem for approach regions complex tangentially broader than admissible ones, in domains of finite type. In Chapter 3 discussing the Lindel\"{o}f principle, we provide some conditions which yield admissible convergence. In Chapter 4 we construct inner functions for a type of domains more general than strongly pseudoconvex ones. Discussion is carried out in \mathbb{C}².

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2011

Author dc:creator

• Min, Baili

Contributors dc:contributor

• Steven Krantz

• Mathematics
• Fatou's theorem
• finite type
• inner function
• Linderlof principle
• several complex variables

Language dc:language

English (en)

DOI

https://doi.org/10.7936/K7S180KC

OAI identifier oai:identifier

oai:openscholarship.wustl.edu:etd-1246