Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2007, October 9.

Abstract:
Peano differentiability generalizes ordinary differentiability to higher order. There are two ways to define Peano differentiability for functions defined on non-open sets. For both concepts, we investigate the question under which conditions a function defined on a closed set can be extended to a Peano differentiable function on the ambient space if the sets and functions are definable in an o-minimal structure expanding a real closed field.

Mathematics Subject Classification (2000): 03C64, 14P99, 26B05, 46G05.

Keywords and Phrases: o-minimal structure, Peano derivative, extensions.

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