Real Algebraic and Analytic Geometry
Submission: 2004, June 8.
Text: Suppose (n,d) is such that there exist positive semidefinite forms p of degree d in n variables which are not a sum of squares. We show that there does not exist a finite set of non-zero forms H so that if p is positive semidefinite, then h*p is a sum of squares of forms for some h in H. This paper will appear in the Proceedings of the American Mathematical Society.
Mathematics Subject Classification (2000): 11E76, 11E25.
Keywords and Phrases: Hilbert's 17th problem, denominators, sums of squares.
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