RT Journal Article
T1 The strict Positivstellensatz for global analytic functions and the moment problem for semianalytic sets
A1 Acquistapace, Francesca
A1 Andradas Heranz, Carlos
A1 Broglia, Fabrizio
AB Analytic functions strictly positive on a global semianalytic set X = {f1  0, · · · , fk  0} in Rnare characterized as functions expressible as g = a0+a1f1+· · ·+akfk for strictly positive global analytic functions a0, · · · , ak. The proof is elementary, using the fact that the analytic functions are dense in C(Rn,R) in the Whitney topology. The same proof works for Nash functions. This is an improvement of the standard analytic version of Stengle’s Positivstellensatz in two directions: The hypothesis is weaker (there is no requirement that X be compact) and the conclusion is stronger. Several applications are given including: (i) a new proof of the weak Positivstellensatz for semianalytic sets; and (ii)  the solution of theK-moment problem for basic closed semianalytic
PB Springer
SN 0025-5831
YR 2000
FD 2000
LK https://hdl.handle.net/20.500.14352/57155
UL https://hdl.handle.net/20.500.14352/57155
LA eng
NO GNSAGA
NO CNR
NO MURST
NO DGES
DS Docta Complutense
RD 8 abr 2025