{"id":{"repo_id":"passau-thes","oai_identifier":"oai:kobv.de-opus4-uni-passau:1069"},"canonical_url":"https://search.dev.ndltd.org/etd/passau-thes/oai:kobv.de-opus4-uni-passau:1069","repository":{"repo_id":"passau-thes","name":"Universität Passau","base_url":"https://opus4.kobv.de/opus4-uni-passau/oai"},"display":{"title":"Holomorphic Extensions in the Structure R_{an,exp}","abstract":"In this thesis we consider real analytic functions, i.e. functions which can be described locally as convergent power series and ask the following: Which real analytic functions definable in R_{an,exp} have a holomorphic extension which is again definable in R_{an,exp}? Finding a holomorphic extension is of course not difficult simply by power series expansion. The difficulty is to construct it in a definably way. We will not answer the question above completely, but introduce a large non trivial class of definable functions in R_{an,exp} where for example functions which are iterated compositions from either side of globally subanalytic functions and the global logarithm are contained. We call them restricted log-exp-analytic. After giving some preliminary results like preparation theorems and Tamm's Theorem for this class of functions we are able to show that real analytic restricted log-exp-analytic functions have a holomorphic extension which is again restricted log-exp-analytic.","abstract_html":"In this thesis we consider real analytic functions, i.e. functions which can be described locally as convergent power series and ask the following: Which real analytic functions definable in R_{an,exp} have a holomorphic extension which is again definable in R_{an,exp}? Finding a holomorphic extension is of course not difficult simply by power series expansion. The difficulty is to construct it in a definably way. We will not answer the question above completely, but introduce a large non trivial class of definable functions in R_{an,exp} where for example functions which are iterated compositions from either side of globally subanalytic functions and the global logarithm are contained. We call them restricted log-exp-analytic. After giving some preliminary results like preparation theorems and Tamm's Theorem for this class of functions we are able to show that real analytic restricted log-exp-analytic functions have a holomorphic extension which is again restricted log-exp-analytic.","abstract_has_math":false,"creators":["Opris, Andre"],"institution":"Universität Passau","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Kaiser, Tobias","Peterzil, Kobi"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-03-24","date_published":"2022-03-24","updated_at":"2026-07-24T03:45:06Z","subjects":["O-Minimality","Preparation Theorems","Restricted Log-Exp-Analytic Functions","Complexification","Tamm's Theorem"],"languages":[],"rights":["Standardbedingung laut Einverständniserklärung"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1069","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kaiser, Tobias","Peterzil, Kobi"]},{"key":"dc:creator","label":"Author","values":["Opris, Andre"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universität Passau"]},{"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 Passau"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["O-Minimality","Preparation Theorems","Restricted Log-Exp-Analytic Functions","Complexification","Tamm's Theorem"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Standardbedingung laut Einverständniserklärung"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we consider real analytic functions, i.e. functions which can be described locally as convergent power series and ask the following: Which real analytic functions definable in R_{an,exp} have a holomorphic extension which is again definable in R_{an,exp}? Finding a holomorphic extension is of course not difficult simply by power series expansion. The difficulty is to construct it in a definably way. We will not answer the question above completely, but introduce a large non trivial class of definable functions in R_{an,exp} where for example functions which are iterated compositions from either side of globally subanalytic functions and the global logarithm are contained. We call them restricted log-exp-analytic. After giving some preliminary results like preparation theorems and Tamm's Theorem for this class of functions we are able to show that real analytic restricted log-exp-analytic functions have a holomorphic extension which is again restricted log-exp-analytic."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Holomorphic Extensions in the Structure R_{an,exp}"]}]}],"canonical_facts":{"dc:contributor":["Kaiser, Tobias","Peterzil, Kobi"],"dc:creator":["Opris, Andre"],"dc:description.abstract":["In this thesis we consider real analytic functions, i.e. functions which can be described locally as convergent power series and ask the following: Which real analytic functions definable in R_{an,exp} have a holomorphic extension which is again definable in R_{an,exp}? Finding a holomorphic extension is of course not difficult simply by power series expansion. The difficulty is to construct it in a definably way. We will not answer the question above completely, but introduce a large non trivial class of definable functions in R_{an,exp} where for example functions which are iterated compositions from either side of globally subanalytic functions and the global logarithm are contained. We call them restricted log-exp-analytic. After giving some preliminary results like preparation theorems and Tamm's Theorem for this class of functions we are able to show that real analytic restricted log-exp-analytic functions have a holomorphic extension which is again restricted log-exp-analytic."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Passau"],"dc:rights":["Standardbedingung laut Einverständniserklärung"],"dc:subject":["O-Minimality","Preparation Theorems","Restricted Log-Exp-Analytic Functions","Complexification","Tamm's Theorem"],"dc:title":["Holomorphic Extensions in the Structure R_{an,exp}"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Passau"]},"updated_at":"2026-07-24T03:45:06Z"}