
Positive Polynomials and Sums of Squares
Murray Marshall(Author)
American Mathematical Society (Publisher)
Published in April 2008
Book
Hardback
187 pages
978-0-8218-4402-1 (ISBN)
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
College/higher education
Professional and scholarly
Illustrations
Illustrations
ISBN-13
978-0-8218-4402-1 (9780821844021)
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Schweitzer Classification
Content
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.