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.
Author: | Andreas Fischer |
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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 |