Real Algebraic and Analytic Geometry
Submission: 2004, June 8.
This paper discusses representation theorems for positive polynomials in the plane. We consider six related types of implications for the six types of products of closed intervals in the plane, through an extensive analysis of the literature and a few new theorems. (This paper will appear in "Positive polynomials in Control" (A. Garulli, D. Henrion eds.), Springer Lecture Notes in Control and Information Sciences.
Mathematics Subject Classification (2000): 12D99, 26C99.
Keywords and Phrases: Positive polynomials, Schmudgen's Theorem, sums of squares.
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