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On Hilbert's 17th Problem for global analytic functions indimension 3.

Fernando Galván, José Francisco (2008) On Hilbert's 17th Problem for global analytic functions indimension 3. Commentarii Mathematici Helvetici , 83 (1). pp. 67-100. ISSN 0010-2571

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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 special. 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, but we also find some sufficient conditions to get finite 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 sums of squares.

Item Type:Article
Uncontrolled Keywords:Hilbert’s 17th Problem; Sum of squares; Irreducible factors; Special factors.
Subjects:Sciences > Mathematics > Number theory
ID Code:15125
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