{"id":{"repo_id":"wustl","oai_identifier":"oai:openscholarship.wustl.edu:etd-1246"},"canonical_url":"https://search.dev.ndltd.org/etd/wustl/oai:openscholarship.wustl.edu:etd-1246","repository":{"repo_id":"wustl","name":"Washington University in St. Louis","base_url":"https://openscholarship.wustl.edu/do/oai/"},"display":{"title":"The Boundary Behavior of Holomorphic Functions","abstract":"In the theory of several complex variables, the Fatou type problems, the Lindel\\\"{o}f principle, and inner functions have been well studied for strongly pseudoconvex domains. In this thesis, we are going to study more generalized domains, those of finite type. In Chapter 2 we show that there is no Fatou's theorem for approach regions complex tangentially broader than admissible ones, in domains of finite type. In Chapter 3 discussing the Lindel\\\"{o}f principle, we provide some conditions which yield admissible convergence. In Chapter 4 we construct inner functions for a type of domains more general than strongly pseudoconvex ones. Discussion is carried out in $\\mathbb{C}^2$.","abstract_html":"In the theory of several complex variables, the Fatou type problems, the Lindel\\&quot;{o}f principle, and inner functions have been well studied for strongly pseudoconvex domains. In this thesis, we are going to study more generalized domains, those of finite type. In Chapter 2 we show that there is no Fatou&#x27;s theorem for approach regions complex tangentially broader than admissible ones, in domains of finite type. In Chapter 3 discussing the Lindel\\&quot;{o}f principle, we provide some conditions which yield admissible convergence. In Chapter 4 we construct inner functions for a type of domains more general than strongly pseudoconvex ones. Discussion is carried out in <span class=\"etd-inline-math\">\\mathbb{C}<sup>2</sup></span>.","abstract_has_math":true,"creators":["Min, Baili"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Steven Krantz"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-01-01T08:00:00Z","date_published":"2011-01-01T08:00:00Z","updated_at":"2026-07-24T06:12:58Z","subjects":["Mathematics","Fatou's theorem","finite type","inner function","Linderlof principle","several complex variables"],"languages":["English (en)"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K7S180KC"],"render_values":[{"text":"https://doi.org/10.7936/K7S180KC","href":"https://doi.org/10.7936/K7S180KC","code":true}]}]},"links":{"outbound_url":"https://openscholarship.wustl.edu/etd/247","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Steven Krantz"]},{"key":"dc:creator","label":"Author","values":["Min, Baili"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2010-01-01T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Fatou's theorem","finite type","inner function","Linderlof principle","several complex variables"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/etd/247"]},{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K7S180KC"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In the theory of several complex variables, the Fatou type problems, the Lindel\\\"{o}f principle, and inner functions have been well studied for strongly pseudoconvex domains. In this thesis, we are going to study more generalized domains, those of finite type. In Chapter 2 we show that there is no Fatou's theorem for approach regions complex tangentially broader than admissible ones, in domains of finite type. In Chapter 3 discussing the Lindel\\\"{o}f principle, we provide some conditions which yield admissible convergence. In Chapter 4 we construct inner functions for a type of domains more general than strongly pseudoconvex ones. Discussion is carried out in $\\mathbb{C}^2$."]},{"key":"dc:title","label":"Title","values":["The Boundary Behavior of Holomorphic Functions"]}]}],"canonical_facts":{"dc:contributor":["Steven Krantz"],"dc:creator":["Min, Baili"],"dc:date.available":["2010-01-01T08:00:00Z"],"dc:description.abstract":["In the theory of several complex variables, the Fatou type problems, the Lindel\\\"{o}f principle, and inner functions have been well studied for strongly pseudoconvex domains. In this thesis, we are going to study more generalized domains, those of finite type. In Chapter 2 we show that there is no Fatou's theorem for approach regions complex tangentially broader than admissible ones, in domains of finite type. In Chapter 3 discussing the Lindel\\\"{o}f principle, we provide some conditions which yield admissible convergence. In Chapter 4 we construct inner functions for a type of domains more general than strongly pseudoconvex ones. Discussion is carried out in $\\mathbb{C}^2$."],"dc:identifier":["https://openscholarship.wustl.edu/etd/247"],"dc:identifier.doi":["https://doi.org/10.7936/K7S180KC"],"dc:language":["English (en)"],"dc:subject":["Mathematics","Fatou's theorem","finite type","inner function","Linderlof principle","several complex variables"],"dc:title":["The Boundary Behavior of Holomorphic Functions"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T06:12:58Z"}