Real Algebraic and Analytic Geometry
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276. Andreas Fischer:
Infinite Peano differentiable functions in polynomially bounded o-minimal structures.

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Submission: 2009, March 31.

Abstract:
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.

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