Positive Polynomials: From Hilbert’s 17th Problem to Real Algebra

By A. Prestel, Charles N. Delzell. 2001

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A tutorial on sum of squares techniques for systems analysis (2005, background): “There is a wealth of literature on SOS and positive polynomials, especially after Hilbert’s 17th problem [49] was answered affirmatively by Artin in 1926, a development that formed the foundation of real algebra and real algebraic geometry [48], [4].”
Sums of Squares, Moment Matrices and Optimization Over Polynomials (2009, methodology): “For a more advanced exposition on positivity and sums of squares and links to the moment problem, we refer in particular to the article by Scheiderer [125] and Schmüdgen [127] in this volume, to the survey article by Helton and Putinar [52], and to the monographs by Prestel and Delzell [114] and by ”
POSITIVE POLYNOMIALS IN SCALAR AND MATRIX VARIABLES, THE SPECTRAL THEOREM AND OPTIMIZATION (2006, methodology): “on and has remained unknown to the working mathematician until mid XX-th Century. His articles are available now from a variety of parallel sources, see for instance [T86] and the historical notes in [PD01]. His main thesis is contained in the following principle, cited from his original 1948 RAND p”