Peano-differentiable functions in O-Minimal structures
Peano-differenzierbare Funktionen in o-minimalen Strukturen
- We discuss several aspects of Peano-differentiable functions which are definable in an o-minimal structure expanding a real closed field. After recalling some already known results about o-minimal structures we develop techniques for the intrinsic study of differentiable functions in these structures. After this we study (ordinary) differentiable functions definable in an o-minimal structure and their continuiuty properties along curves of different differentiability classes. Then we generalise (ordinary) differentiability to Peano-differentiability. We study differentiability of certain Peano-derivatives of definable functions and characterise the sets of non-continuity of these derivatives. In the end we study extendability of these functions defined on closed sets and give sufficient conditions by which we can extend functions as Peano-differentiable functions.
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| Author: | Andreas Fischer |
|---|---|
| URN: | urn:nbn:de:bvb:739-opus-673 |
| Advisor: | Niels Schwartz |
| Document Type: | Doctoral Thesis |
| Language: | English |
| Year of Completion: | 2005 |
| Date of Publication (online): | 2006/03/08 |
| Publishing Institution: | Universität Passau |
| Granting Institution: | Universität Passau, Fakultät für Informatik und Mathematik |
| Date of final exam: | 2006/02/09 |
| Release Date: | 2006/03/08 |
| Tag: | Peano-differenzierbare Funktion; o-minimale Struktur Peano-differentiable function; o-minimal structure |
| GND Keyword: | Semialgebraische Menge; Reelle Analysis; Reell-abgeschlossener Körper; Differenzierbare Funktion; Reelle algebraische Geometrie |
| Institutes: | Fakultät für Informatik und Mathematik / Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| MSC-Classification: | 14-XX ALGEBRAIC GEOMETRY / 14Pxx Real algebraic and real analytic geometry / 14P99 None of the above, but in this section |
| open_access (DINI-Set): | open_access |
| Licence (German): |  Standardbedingung laut Einverständniserklärung |
