Abstract
In this note we prove two Positivstellensätze for definable functions of class $C^r$, $0\le r < \infty$, in any $o$-minimal structure $\mathcal{S}$ expanding a real closed field $R$. Namely, we characterize the definable functions that are nonnegative (resp. strictly positive) on basic definable sets of the form $F=\{f_1\ge 0,\dots, f_k\ge 0\}$.
Citation
F. Acquistapace. C. Andradas. F. Broglia. "The Positivstellensatz for definable functions on o-minimal structures." Illinois J. Math. 46 (3) 685 - 693, Fall 2002. https://doi.org/10.1215/ijm/1258130979
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