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Acquistapace, Francesca ; Broglia, Fabrizio ; Fernando Galván, José Francisco | Springer Verlag | 2009We consider several modified versions of the Positivstellensatz for global analytic functions that involve infinite sums of squares and/or positive semidefinite analytic functions. We obtain a general local-global criterion which localizes the o[...]texto impreso
Acquistapace, Francesca ; Broglia, Fabrizio ; Fernando Galván, José Francisco | Springer | 2015-12-17In this work we present the concept of C-semianalytic subset of a real analytic manifold and more generally of a real analytic space. C-semianalytic sets can be understood as the natural generalization to the semianalytic setting of global analy[...]texto impreso
Acquistapace, Francesca ; Broglia, Fabrizio ; Fernando Galván, José Francisco | SCUOLA NORMALE SUPERIORE DI PISA | 2014In this work, we present "infinite" multiplicative formulae for countable collections of sums of squares (of meromorphic functions on R-n). Our formulae generalize the classical Pfister's ones concerning the representation as a sum of 2(r) squar[...]texto impreso
Acquistapace, Francesca ; Broglia, Fabrizio ; Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María | French Mathematical Society | 2010We consider the 17(th) Hilbert Problem for global real analytic functions in a modified form that involves infinite sums of squares. Then we prove a local-global principle for a real global analytic function to be a sum of squares of global real[...]texto impreso
Acquistapace, Francesca ; Broglia, Fabrizio ; Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María | 2004-01-26We consider Hilbert’s 17 problem for global analytic functions in a modified form that involves infinite sums of squares. This reveals an essential connection between the solution of the problem and the computation of Pythagoras numbers of merom[...]texto impreso
Acquistapace, Francesca ; Broglia, Fabrizio ; Fernando Galván, José Francisco | American Mathematical Society | 2016In this work we prove the real Nullstellensatz for the ring O(X) of analytic functions on a C-analytic set X ? Rn in terms of the saturation of ?ojasiewicz’s radical in O(X): The ideal I(?(a)) of the zero-set ?(a) of an ideal a of O(X) coincides[...]texto impreso
We show that the Pythagoras number of a real analytic curve is the supremum of the Pythagoras numbers of its singularities, or that supremum plus 1. This includes cases when the Pythagoras number is infinite.texto impreso
Acquistapace, Francesca ; Broglia, Fabrizio ; Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María | Société Mathématique de France | 2005We show that (i) every positive semidefinite meromorphic function germ on a surface is a sum of 4 squares of meromorphic function germs, and that (ii) every positive semidefinite global meromorphic function on a normal surface is a sum of 5 squa[...]texto impreso
Acquistapace, Francesca ; Andradas Heranz, Carlos ; Broglia, Fabrizio | American Mathematical Society | 1999We study the problem of deciding whether two disjoint semialgebraic sets of an algebraic variety over R are separable by a polynomial. For that we isolate a dense subfamily of spaces of orderings, named geometric, which suffice to test separatio[...]texto impreso
Acquistapace, Francesca ; Andradas Heranz, Carlos ; Broglia, Fabrizio | University of Illinois | 2002In this note we prove two Positivstellensatze for definable functions of class C-r, 0 less than or equal to rtexto impreso
Analytic functions strictly positive on a global semianalytic set X = {f1 0, · · · , fk 0} in Rn are characterized as functions expressible as g = a0+a1f1+· · ·+akfk for strictly positive global analytic functions a0, · · · , ak. The proof is [...]
