{"id":{"repo_id":"potsdam-diss","oai_identifier":"oai:kobv.de-opus4-uni-potsdam:10364"},"canonical_url":"https://search.dev.ndltd.org/etd/potsdam-diss/oai:kobv.de-opus4-uni-potsdam:10364","repository":{"repo_id":"potsdam-diss","name":"Universität Potsdam - Diss","base_url":"https://publishup.uni-potsdam.de/opus4-ubp/oai"},"display":{"title":"Operators on singular manifolds","abstract":"We study the interplay between analysis on manifolds with singularities and complex analysis and develop new structures of operators based on the Mellin transform and tools for iterating the calculus for higher singularities. We refer to the idea of interpreting boundary value problems (BVPs) in terms of pseudo-differential operators with a principal symbolic hierarchy, taking into account that BVPs are a source of cone and edge operator algebras. The respective cone and edge pseudo-differential algebras in turn are the starting point of higher corner theories. In addition there are deep relationships between corner operators and complex analysis. This will be illustrated by the Mellin symbolic calculus.","abstract_html":"We study the interplay between analysis on manifolds with singularities and complex analysis and develop new structures of operators based on the Mellin transform and tools for iterating the calculus for higher singularities. We refer to the idea of interpreting boundary value problems (BVPs) in terms of pseudo-differential operators with a principal symbolic hierarchy, taking into account that BVPs are a source of cone and edge operator algebras. The respective cone and edge pseudo-differential algebras in turn are the starting point of higher corner theories. In addition there are deep relationships between corner operators and complex analysis. This will be illustrated by the Mellin symbolic calculus.","abstract_has_math":false,"creators":["Lyu, Xiaojing"],"institution":"Universität Potsdam","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Schulze, Bert-Wolfgang"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-02-17","date_published":"2017-02-17","updated_at":"2026-07-24T03:51:58Z","subjects":["order filtration","Mellin-Symbols","singular manifolds","Ordnungs-Filtrierung","Mellin-Symbole","singuläre Mannigfaltigkeiten"],"languages":[],"rights":["CC-BY - Namensnennung 4.0 International"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://publishup.uni-potsdam.de/frontdoor/index/index/docId/10364","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Schulze, Bert-Wolfgang"]},{"key":"dc:creator","label":"Author","values":["Lyu, Xiaojing"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universität Potsdam"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Potsdam"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["order filtration","Mellin-Symbols","singular manifolds","Ordnungs-Filtrierung","Mellin-Symbole","singuläre Mannigfaltigkeiten"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["CC-BY - Namensnennung 4.0 International"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We study the interplay between analysis on manifolds with singularities and complex analysis and develop new structures of operators based on the Mellin transform and tools for iterating the calculus for higher singularities. We refer to the idea of interpreting boundary value problems (BVPs) in terms of pseudo-differential operators with a principal symbolic hierarchy, taking into account that BVPs are a source of cone and edge operator algebras. The respective cone and edge pseudo-differential algebras in turn are the starting point of higher corner theories. In addition there are deep relationships between corner operators and complex analysis. This will be illustrated by the Mellin symbolic calculus.","Wir studieren den Zusammenhang zwischen Analysis auf Mannigfaltigkeiten mit Singularitäten und komplexer Analysis und entwickeln neue Strukturen von Operatoren basierend auf der Mellin-Transformation und Hilfsmitteln für die Iteration des Kalküls für höhere Singularitäten. Wir beziehen uns auf die Idee von der Interpretation von Randwert-Problemen (BVPs) durch Pseudo-Differential-operatoren und Hauptsymbol-Hierarchien, unter Berüksichtigung der Tatsache, dass BVPs eine Quelle von Konus- und Kanten-Operator- algebren sind. Die betreffenden Konus- und Kanten-Pseudo-differentiellen Algebren sind wiederum der Startpunkt von höheren Eckentheorien. Zusätzlich bestehen tiefe Beziehungen zwischen Ecken-Operatoren und komplexer Analysis. Dies wird illustiert durch den Mellin-Symbol Kalkül."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Operators on singular manifolds","Operatoren auf singuläre Mannigfaltigkeiten"]}]}],"canonical_facts":{"dc:contributor":["Schulze, Bert-Wolfgang"],"dc:creator":["Lyu, Xiaojing"],"dc:description.abstract":["We study the interplay between analysis on manifolds with singularities and complex analysis and develop new structures of operators based on the Mellin transform and tools for iterating the calculus for higher singularities. We refer to the idea of interpreting boundary value problems (BVPs) in terms of pseudo-differential operators with a principal symbolic hierarchy, taking into account that BVPs are a source of cone and edge operator algebras. The respective cone and edge pseudo-differential algebras in turn are the starting point of higher corner theories. In addition there are deep relationships between corner operators and complex analysis. This will be illustrated by the Mellin symbolic calculus.","Wir studieren den Zusammenhang zwischen Analysis auf Mannigfaltigkeiten mit Singularitäten und komplexer Analysis und entwickeln neue Strukturen von Operatoren basierend auf der Mellin-Transformation und Hilfsmitteln für die Iteration des Kalküls für höhere Singularitäten. Wir beziehen uns auf die Idee von der Interpretation von Randwert-Problemen (BVPs) durch Pseudo-Differential-operatoren und Hauptsymbol-Hierarchien, unter Berüksichtigung der Tatsache, dass BVPs eine Quelle von Konus- und Kanten-Operator- algebren sind. Die betreffenden Konus- und Kanten-Pseudo-differentiellen Algebren sind wiederum der Startpunkt von höheren Eckentheorien. Zusätzlich bestehen tiefe Beziehungen zwischen Ecken-Operatoren und komplexer Analysis. Dies wird illustiert durch den Mellin-Symbol Kalkül."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Potsdam"],"dc:rights":["CC-BY - Namensnennung 4.0 International"],"dc:subject":["order filtration","Mellin-Symbols","singular manifolds","Ordnungs-Filtrierung","Mellin-Symbole","singuläre Mannigfaltigkeiten"],"dc:title":["Operators on singular manifolds","Operatoren auf singuläre Mannigfaltigkeiten"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Potsdam"]},"updated_at":"2026-07-24T03:51:58Z"}