Acquistapace, FrancescaBroglia, FabrizioFernando Galván, José Francisco2023-06-192023-06-1920140391-173Xhttps://hdl.handle.net/20.500.14352/33652In 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) squares of the product of two elements of a field K which are sums of 2(r) squares. As a main application, we reduce the representation of a positive semidefinite analytic function on R-n 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 R-n which has just one complex irreducible factor and whose zeroset has dimension between 1 and n - 2.engjournal articlerestricted access51MathematicsMatemáticas (Matemáticas)12 Matemáticas