TY - THES A1 - Opris, Andre T1 - Holomorphic Extensions in the Structure R_{an,exp} N2 - 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. KW - O-Minimality KW - Preparation Theorems KW - Restricted Log-Exp-Analytic Functions KW - Complexification KW - Tamm's Theorem KW - O-Minimalität Y1 - 2022 UR - https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1069 UR - https://nbn-resolving.org/urn:nbn:de:bvb:739-opus4-10691 ER -