Date of Award

1-1-2010

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (iv, 81 pages) : illustrations.

Dissertation/Thesis Chair

Donald Wilken

Committee Members

Kehe Zhu, Ronwei Yang, Michael R Range

Keywords

Analytic functions, Convex functions, Integrals, Generalized

Subject Categories

Physical Sciences and Mathematics

Abstract

A function f in Fis an extreme point of F if f can not be written as a proper convex combination of two distinct elements of F. We will investigate extreme points and non-extreme points of compact convex family of analytic function on the open unit disc which are generated by integrating a function against a probability measure on torus. A function f in F is a generalized exposed point if f uniquely maximizes real part of L over F for some generalized linear functional L. We use the fact that if f is a generalized exposed point of F, then f is an extreme point of F to find extreme points.

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