Real Algebraic and Analytic Geometry

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276. Andreas Fischer:
Infinite Peano differentiable functions in polynomially bounded o-minimal structures.


Submission: 2009, March 31.

Let $\mathfrak{R}$ be an o-minimal expansion of a real closed field. We show that the definable infinitely Peano differentiable functions are smooth if and only if $\mathfrak{R}$ is polynomially bounded.

Mathematics Subject Classification (2000): 03C64, 26E10, 58C20.

Keywords and Phrases: Peano differentiable function, smooth function, polynomially bounded o-minimal structure.

Full text, 5p.: dvi 24k, ps.gz 127k, pdf 162k.

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