Author's Department/Program
Mathematics
Language
English (en)
Date of Award
January 2011
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Chair and Committee
Steven Krantz
Abstract
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 $\mathbb{C}^2$.
Recommended Citation
Min, Baili, "The Boundary Behavior of Holomorphic Functions" (2011). All Theses and Dissertations (ETDs). 247.
https://openscholarship.wustl.edu/etd/247
Comments
Permanent URL: http://dx.doi.org/10.7936/K7S180KC