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EnglishAbstract. 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.
| Autori interni: | |
| Autori: | Francesca Acquistapace; Fabrizio Broglia; Jose F. Fernando |
| Titolo: | On Hilbert's 17th problem and Pfister's multiplicative formulae for the ring of real analytic functions |
| Anno del prodotto: | 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. |
| Digital Object Identifier (DOI): | 10.2422/2036-2145.201201_004 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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