Certificates of Positivity for Real Polynomials: Theory, Practice, and Applications

This book collects and explains the many theorems concerning the existence of certificates of positivity for polynomials that are positive globally or on semialgebraic sets. A certificate of positivity for a real polynomial is an algebraic identity that gives an immediate proof of a positivity condition for the polynomial. Certificates of positivity have their roots in fundamental work of David Hilbert from the late 19^th century on positive polynomials and sums of squares. Because of the nu...