Resumen de On Hilbert's 17th problem and Pfister's multiplicative formulae for the ring of real analytic functions
Francesca Acquistapace, F. Broglia, José Francisco Fernando Galván
In this work, we present “infinite” multiplicative formulae for countable collections of sums of squares (of meromorphic functions on Rn). Our formulae generalize the classical Pfister’s ones concerning the representation as a sum of 2r squares of the product of two elements of a field K which are sums of 2r squares. As a main application, we reduce the representation of a positive semidefinite analytic function on Rn as a sum of squares to the representation as sums of squares of its special factors. Recall that roughly speaking a special factor is an analytic function on Rn which has just one complex irreducible factor and whose zeroset has dimension between 1 and n − 2.
