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Positive semidefinite polynomials and sums of squares. (English) Zbl 0762.11018

The paper considers the question of Hilbert, whether a positive semidefinite real polynomial of two real variables is a sum of squares. Hilbert’s answer and later refinements by Choi, Lam, Reznick and Rosenberg are partially proved and refined further.

MSC:

11E76 Forms of degree higher than two
11E25 Sums of squares and representations by other particular quadratic forms
26C99 Polynomials, rational functions in real analysis
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