{"id":{"repo_id":"wichita-thes","oai_identifier":"oai:soar.wichita.edu:10057/10606"},"canonical_url":"https://search.dev.ndltd.org/etd/wichita-thes/oai:soar.wichita.edu:10057/10606","repository":{"repo_id":"wichita-thes","name":"Wichita State University","base_url":"https://soar.wichita.edu/oai/request"},"display":{"title":"On convergence sets of formal power series","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Al-Shutnawi, Basma"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-12","date_published":"2013-12","updated_at":"2026-07-24T06:05:36Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/10606"],"render_values":[{"text":"hdl:10057/10606","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2013-12"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10057/10606"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["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."]},{"key":"dc:title","label":"Title","values":["On convergence sets of formal power series"]}]}],"canonical_facts":{"dc:date.issued":["2013-12"],"dc:description.other":["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:identifier":["hdl:10057/10606"],"dc:title":["On convergence sets of formal power series"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T06:05:36Z"}