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Positivstellensätze for differentiable functions

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Abstract

We present a canonical proof of both the strict and weak Positivstellensatz for rings of differentiable and smooth functions. Our construction is explicit, preserves definability in expansions of the real field, and it works in definably complete expansions of real closed fields as well as for real-valued functions on Banach spaces.

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Author notes

  1. Andreas Fischer

    Present address: Gymnasium St. Ursula Dorsten, 46282, Dorsten, Germany

Authors and Affiliations

  1. Fields Institute, 222 College Street, Toronto, ON, M5T3J1, Canada

    Andreas Fischer

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  1. Andreas Fischer
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Correspondence to Andreas Fischer.

Additional information

The author has been supported by the Thematic Program on o-minimal Structures and Real Analytic Geometry of the Fields Institute.

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Fischer, A. Positivstellensätze for differentiable functions. Positivity 15, 297–307 (2011). https://doi.org/10.1007/s11117-010-0077-5

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  • DOI: https://doi.org/10.1007/s11117-010-0077-5

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