On convergence sets of formal power series

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Al-Shutnawi, Basma
Issue Date
2013-12
Type
Dissertation
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en_US
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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.

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Thesis (Ph.D.)--Wichita State University, Fairmount College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics and Physics
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Wichita State University
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Copyright 2013 Basma Al-Shutnawi
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