Acquistapace, FrancescaAndradas Heranz, CarlosBroglia, Fabrizio2023-06-202023-06-2020020019-2082https://hdl.handle.net/20.500.14352/57152In 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}.engjournal articlehttps://www.projecteuclid.org/euclid.ijm/1258130979restricted access512.7Positivstellensatzdefinable functionso-minimal structurereal closed fieldGeometria algebraica1201.01 Geometría Algebraica