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On Hilbert's 17th problem and Pfister's multiplicative formulae for the ring of real analytic functions

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Acquistapace, Francesca and Broglia, Fabrizio and Fernando Galván, José Francisco (2014) On Hilbert's 17th problem and Pfister's multiplicative formulae for the ring of real analytic functions. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 13 (2). pp. 333-369. ISSN 0391-173X

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Abstract

In 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.


Item Type:Article
Uncontrolled Keywords:Mathematics
Subjects:Sciences > Mathematics
ID Code:26872
Deposited On:30 Sep 2014 10:50
Last Modified:30 Sep 2014 10:50

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