{"id":{"repo_id":"wichita-thes","oai_identifier":"oai:null:10057/10606"},"canonical_url":"https://search.dev.ndltd.org/etd/wichita-thes/oai:null: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":"Wichita State University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Ma, Daowei"],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-12","date_published":"2013-12","updated_at":"2026-08-21T16:50:55Z","subjects":[],"languages":["en_US"],"rights":["Copyright 2013 Basma Al-Shutnawi"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["d13023"],"render_values":[{"text":"d13023","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10057/10606","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://soar.wichita.edu/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Anull%3A10057%2F10606","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Ma, Daowei"]},{"key":"dc:creator","label":"Author","values":["Al-Shutnawi, Basma"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-06-26T14:52:56Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-06-26T14:52:56Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-12"]},{"key":"dc:publisher","label":"Institution","values":["Wichita State University"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2013 Basma Al-Shutnawi"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["d13023"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10057/10606"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph.D.)--Wichita State University, Fairmount College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics and Physics"]},{"key":"dc:description.abstract","label":"Abstract","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:contributor.advisor":["Ma, Daowei"],"dc:creator":["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: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:identifier.other":["d13023"],"dc:identifier.uri":["http://hdl.handle.net/10057/10606"],"dc:language.iso":["en_US"],"dc:publisher":["Wichita State University"],"dc:rights":["Copyright 2013 Basma Al-Shutnawi"],"dc:title":["On convergence sets of formal power series"],"dc:type":["Dissertation"]},"updated_at":"2026-08-21T16:50:55Z"}