Virginia Tech
Two problems in function theory of one complex variable: local properties of solutions of second-order differential equations and number of deficient functions of some entire functions
Abstract
dc:description.abstractThis dissertation investigates two problems in the function theory of one complex variable. In Chapter 1, we study the asymptotics and zero distribution of solutions of the differential equation w<sup>n</sup> + A(z)w = 0, where A(z) is a transcendental entire function of very slow growth. The result parallels the classical case when A(z) is assumed to be a polynomial. An analogue concerning the case when A(z) is a transcendental entire function whose series expansion satisfies the Hadamard gap condition is given. In Chapter 2, we give upper bounds for the number of deficient functions of entire functions of completely regular growth and entire functions whose zeros have angular densities. In particular, the bound is 2λ + 1 if the entire function is of completely regular growth with order λ, 0 < λ < ∞.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 1994
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Cheng, Jiuyi
- Chair dc:contributor.committeechair
-
- Rossi, John F.
- Committee members dc:contributor.committeemember
-
- Murray, M. M.
- Olin, Robert F.
- Snider, Robert L.
- Wheeler, Robert L.
Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-06072006-124203
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/38553