@phdthesis{Opris2022, author = {Opris, Andre}, title = {Holomorphic Extensions in the Structure R_{an,exp}}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:739-opus4-10691}, school = {Universit{\"a}t Passau}, pages = {233 Seiten}, year = {2022}, 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.}, subject = {O-Minimalit{\"a}t}, language = {en} }