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.
| Author: | Andre Opris |
|---|---|
| URN: | urn:nbn:de:bvb:739-opus4-10691 |
| Advisor: | Tobias Kaiser, Kobi Peterzil |
| Document Type: | Doctoral Thesis |
| Language: | English |
| Year of Completion: | 2022 |
| Date of Publication (online): | 2022/05/19 |
| Date of first Publication: | 2022/05/19 |
| Publishing Institution: | Universität Passau |
| Granting Institution: | Universität Passau, Fakultät für Informatik und Mathematik |
| Date of final exam: | 2022/03/24 |
| Release Date: | 2022/05/19 |
| Tag: | Complexification; O-Minimality; Preparation Theorems; Restricted Log-Exp-Analytic Functions; Tamm's Theorem |
| GND Keyword: | O-MinimalitätGND |
| Page Number: | 233 Seiten |
| Institutes: | Fakultät für Informatik und Mathematik |
| Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 000 Informatik, Informationswissenschaft, allgemeine Werke |
| open_access (DINI-Set): | open_access |
| Licence (German): | Standardbedingung laut Einverständniserklärung |

