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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.

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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):License LogoStandardbedingung laut Einverständniserklärung