On convergence sets of formal power series

In this thesis we consider the convergence sets of formal power series of the form f(z, t)=sigma infinity j=0 pj(z)tj, where pj(z) are polynomials. A subset E of the complex plane C is said to be a convergence set if there is a series f(z, t)=sigma infinity j=0 pj(z)tj such that E is exactly the set of points z for which f(z, t) converges as a power series in t. A quasi-simply connected set is defined to be the union of a countable collection of polynomially convex compact sets. We prove that a subset of C is a convergence set if and only if it is a quasi-simply-connected set. We also give an example of a compact set which is not a convergence set.

Grantor dc:publisher

Wichita State University

Year dc:date.issued

2013

Author dc:creator

• Al-Shutnawi, Basma

Advisor dc:contributor.advisor

• Ma, Daowei

Statement dc:rights

• Copyright 2013 Basma Al-Shutnawi

Language dc:language.iso

en_US

Dc Identifier Other

d13023

OAI record oai:identifier

https://soar.wichita.edu/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Anull%3A10057%2F10606