2026-06-27T22:26:01Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/336522023-08-28T07:37:40Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Acquistapace, Francesca
author
Broglia, Fabrizio
author
Fernando Galván, José Francisco
2023-06-19T13:25:38Z
2023-06-19T13:25:38Z
2014
0391-173X
https://hdl.handle.net/20.500.14352/33652
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.
eng
On Hilbert's 17th problem and Pfister's multiplicative formulae for the ring of real analytic functions
journal article
URL
https://docta.ucm.es/bitstreams/d5c5ffb8-e8e8-4397-8709-17898e030574/download
File
MD5
391d0a80f9c6bab8cc580f9a8eafb530
1015566
application/pdf
FernandoJoseF201.pdf