The Positivstellensatz for definable functions on o-minimal structures
Acquistapace, F. ; Andradas, C. ; Broglia, F.
Illinois J. Math., Tome 46 (2002) no. 3, p. 685-693 / Harvested from Project Euclid
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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 $F=\{f_1\ge 0,\dots, f_k\ge 0\}$.
Publié le : 2002-07-15
Classification:  03C64,  13J30 
@article{1258130979,
     author = {Acquistapace, F. and Andradas, C. and Broglia, F.},
     title = {The Positivstellensatz for definable functions on o-minimal structures},
     journal = {Illinois J. Math.},
     volume = {46},
     number = {3},
     year = {2002},
     pages = { 685-693},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258130979}
}

Acquistapace, F.; Andradas, C.; Broglia, F. The Positivstellensatz for definable functions on o-minimal structures. Illinois J. Math., Tome 46 (2002) no. 3, pp.  685-693. http://gdmltest.u-ga.fr/item/1258130979/