Acquistapace, Francesca and Andradas Heranz, Carlos and Broglia, Fabrizio (2002) The Positivstellensatz for definable functions on O-minimal structures. Illinois Journal of Mathematics, 46 (3). pp. 685-693. ISSN 0019-2082
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Abstract
In this note we prove two Positivstellensatze for definable functions of class C-r, 0 less than or equal to r < &INFIN;, in any o-minimal structure 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,...,f(k) &GE; 0}.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Positivstellensatz; definable functions; o-minimal structure; real closed field |
| Subjects: | Sciences > Mathematics > Algebraic geometry |
| ID Code: | 14764 |
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| Deposited On: | 17 Apr 2012 13:48 |
| Last Modified: | 14 May 2013 15:42 |
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