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Institute
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.