Holomorphic Extensions in the Structure R_{an,exp}

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.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Passau

Year

2022

Author dc:creator

• Opris, Andre

Contributors dc:contributor

• Kaiser, Tobias
• Peterzil, Kobi

• O-Minimality
• Preparation Theorems
• Restricted Log-Exp-Analytic Functions
• Complexification
• Tamm's Theorem

Statement dc:rights

• Standardbedingung laut Einverständniserklärung

Repository record source_url

https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1069

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-passau:1069