"On the location of zeros of solutions to w"" + Aw = 0 for certain entire functions A"

"Consider the differential equation $(\*)$ $w\sp{\prime\prime}$ + $Aw$ = 0 where $A$ is of the form $A$($z$) = $\sum\sbsp{j=1}{m}Q\sb{j}(z)$exp$P\sb{j}(z)$ with $Q\sb{j}$ and $P\sb{j}$ polynomials in $z$. We study the location in the complex plane of the zeros of solutions to $(\*)$. Under mild hypotheses on the $P\sb{j}$'s and $Q\sb{j}$'s, we show that there exist both ""zero-scarce"" regions and ""zero-rich"" regions. We call an unbounded region in the complex plane ""zero-scarce"" if every nontrivial solution of $(\*)$ has only finitely many zeros in the region. In contrast, a region is called ""zero-rich"" if there exists a nontrivial solution of $(\*)$ with infinitely many zeros in the region."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Steinbart, Enid Marguerite

Contributors dc:contributor

• Ting, Tran Wa

• Mathematics

Statement dc:rights

• Copyright 1989 Steinbart, Enid Marguerite

Language dc:language

eng

Identifier

AAI8924947
(UMI)AAI8924947

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/20092