Positive polynomials and sums of squares

Bibliographic Information

Positive polynomials and sums of squares

Murray Marshall

(Mathematical surveys and monographs, v. 146)

American Mathematical Society, c2008

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Note

Includes bibliographical references (p. 183-187)

Description and Table of Contents

Description

The study of positive polynomials brings together algebra, geometry and analysis. The subject is of fundamental importance in real algebraic geometry, when studying the properties of objects defined by polynomial inequalities. Hilbert's 17th problem and its solution in the first half of the 20th century were landmarks in the early days of the subject. More recently, new connections to the moment problem and to polynomial optimization have been discovered. The moment problem relates linear maps on the multidimensional polynomial ring to positive Borel measures.

Table of Contents

Preliminaries Positive polynomials and sums of square Krivine's Positivstellensatz The moment problem Non-compact case Archimedean $T$-modules Schmudgen's Positivstellensatz Putinar's question Weak isotropy of quadratic forms Scheiderer's local-global principle Semidefinite programming and optimization Appendix 1: Tarski-Seidenberg theorem Appendix 2: Algebraic sets Bibiography.

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