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The Positivstellensatz for definable functions on O-minimal structures


Acquistapace, Francesca y Andradas Heranz, Carlos y 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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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}.

Tipo de documento:Artículo
Palabras clave:Positivstellensatz; definable functions; o-minimal structure; real closed field
Materias:Ciencias > Matemáticas > Geometria algebraica
Código ID:14764

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Última Modificación:06 Feb 2014 10:08

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