Peano-differentiable functions in O-Minimal structures

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.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Passau

Year

2006

Author dc:creator

• Fischer, Andreas

Contributors dc:contributor

• Schwartz, Niels

• o-minimale Struktur
• Peano-differenzierbare Funktion
• o-minimal structure
• Peano-differentiable function

Statement dc:rights

• Standardbedingung laut Einverständniserklärung

Repository record source_url

https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/56

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-passau:56