Real Algebraic and Analytic Geometry |

On the Hilbert's 17th Problem for global analytic functions on dimension 3.

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homepage: http://www.uam.es/josefrancisco.fernando

Submission: 2005, September 1.

*Abstract:
Among the invariant factors $g$ of a positive semidefinite analytic
function $f$ on $\R^3$, those $g$ whose zero set $Y$ is a curve are
called \em special\em. We show that if each special $g$ is a sum of
squares of global meromorphic functions on a neighbourhood of $Y$, then
$f$ is a sum of squares of global meromorphic functions. Here sums can
be (convergent) infinite, and we also find some sufficient conditions
to get \em finite \em sums of squares. In addition, we construct
several examples of positive semidefinite analytic functions which are
infinite sums of squares but maybe could not be finite sum of squares.*

Mathematics Subject Classification (2000): 14P99, 11E25, 32B10, 32S05.

Keywords and Phrases: 17th Hilbert Problem, sum of squares, irreducible factors, special factors.

**Full text**, 32p.:
pdf 293k.

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