dc.contributor.advisor Ma, Daowei dc.contributor.author Al-Shutnawi, Basma dc.date.accessioned 2014-06-26T14:52:56Z dc.date.available 2014-06-26T14:52:56Z dc.date.issued 2013-12 dc.identifier.other d13023 dc.identifier.uri http://hdl.handle.net/10057/10606 dc.description Thesis (Ph.D.)--Wichita State University, Fairmount College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics and Physics dc.description.abstract 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. dc.format.extent vii, 22 p. dc.language.iso en_US dc.publisher Wichita State University dc.rights Copyright 2013 Basma Al-Shutnawi dc.subject.lcsh Electronic dissertations dc.title On convergence sets of formal power series dc.type Dissertation
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