Master of Science
Jerry P. King
In the first part of this paper we provide some basic properties of power series and their analytic continuation which are essential in a study of function theory. Then, following E. Hille's Analytic Function Theory, we develop the theory of holomorphy preserving operators. This theory is a useful tool in establishing the classical Hadamard Gap Theorem. Holomorphy preserving operators also prove to be useful in establishing several theorems giving sufficient conditions for overconvergence. We then state and prove several theorems concerning necessary conditions of overconvergence.
Swetits, John J., "Overconvergence for a normal family of analytical functions" (1967). Theses and Dissertations. 3559.