Sums of Squares and Positive Polynomials

Abstract

In most cases, the building blocks of certificates of positivity are sums of squares of polynomials. In this chapter we discuss the theory of positive polynomials and sums of squares, which underlies everything else in the book. This theory has its origins in the work of Hilbert from the late 19th century; Hilbert’s interest in these topics appears to have started when he was an officially appointed “opponent” for Minkowski’s thesis defense on July 30, 1885.