Alt Title

A class of functions in F whose integral is not in F

Publication Date

2008

Document Type

Dissertation/Thesis

First Advisor

Sons, Linda R.

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Mathematical Sciences

LCSH

Functions; Meromorphic

Abstract

For a function f, meromorphic in the complex plane, R. Nevanlinna noted that its characteristic function T( r, f) could be used to categorize f according to its rate of growth as |z| = r approached infinity. If f is a meromorphic function in the unit disk D = {z : |z| < 1}, many value distribution results which are analogous to those for functions defined in the plane may be proved provided [special characters omitted]If class [special characters omitted] is defined to be those functions meromorphic in D for which [special characters omitted]then D. Shea and L. Sons[19] developed properties of functions in [special characters omitted] and showed [special characters omitted] is not closed under integration. In this dissertation we consider the class [special characters omitted] of analytic functions in D which are in [special characters omitted], but have integrals not in [special characters omitted]. We explore characteristics of the class and show some examples. We explore the manner in which these functions behave in comparison with other function classes in the unit disk D. We consider the power series representation for such functions in [special characters omitted] and look at what conditions must be imposed on the coefficients of a power series about zero. We also examine [special characters omitted] in terms of value distribution, proving some results about the number of zeros of functions f ∈ [special characters omitted] as well as those of their integrals. Finally we consider various representations for functions in [special characters omitted], including gap series and Tsuji products.

Comments

Includes bibliographical references (pages 65-66)

Extent

iv, 66 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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