Author's School

Graduate School of Arts & Sciences

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 $\mathbb{C}^2$.

DOI

https://doi.org/10.7936/K7S180KC

Comments

Permanent URL: http://dx.doi.org/10.7936/K7S180KC

Share

COinS