Abstract. 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 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.
On Hilbert's 17th problem and Pfister's multiplicative formulae for the ring of real analytic functions
ACQUISTAPACE, FRANCESCA;BROGLIA, FABRIZIO;
2014
Abstract
Abstract. 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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
