AbstractsMathematics

Peano-differentiable functions in O-Minimal structures

by Andreas Fischer




Institution: Universität Passau
Department: Informatik und Mathematik
Degree: PhD
Year: 2006
Record ID: 1114673
Full text PDF: https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/56


Abstract

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.