This thesis concerns the classes of analytic functions on bounded, n-connected domains known as the Smirnov classes Ep, where p > 0. Functions in these classes satisfy a certain growth condition and have a relationship to the more well known classes of functions known as the Hardy classes Hp. In this thesis I will show how the geometry of a given domain will determine the existence of non-constant analytic functions in Smirnov classes that possess real boundary values. This is a phenomenon that does not occur among functions in the Hardy classes.
The preliminary and background information is given in Chapters 1 and 3 while the main results of this thesis are presented in Chapters 2 and 4. In Chapter 2, I will consider the case of the simply connected domain and the boundary characteristics that allow non-constant analytic functions with real boundary values in certain Smirnov classes. Chapter 4 explores the case of an n-connected domain and the sufficient conditions for which the aforementioned functions exist. In Chapter 5, I will discuss how my results for simply connected domains extend Neuwirth-Newman's Theorem and finish with an open problem for n-connected domains.
| Identifer | oai:union.ndltd.org:USF/oai:scholarcommons.usf.edu:etd-5858 |
| Date | 01 January 2013 |
| Creators | De Castro, Lisa |
| Publisher | Scholar Commons |
| Source Sets | University of South Flordia |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Graduate Theses and Dissertations |
| Rights | default |
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