Abstract

In this work, we present "infinite" multiplicative formulae for countable collections of sums of squares. our formulae generalize the classical Pfisters'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