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Positive Polynomials and Sums of Squares (Mathematical Surveys and Monographs) by Murray A Marshall is a nonfiction available to read on EtoBox.

What is Positive Polynomials and Sums of Squares (Mathematical Surveys and Monographs) about?

<p>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. This book provides an elementary introduction to positive polynomials and sums of squares, the relationship to the moment problem, and the application to polynomial optimization. The focus is on the exciting new developments that have taken place in the last 15 years, arising out of Schmudgen's solution to the moment problem in the compact case in 1991. The book is accessible to a well-motivated student at the beginning graduate level. The objects being dealt with are concrete and down-to-earth, namely polynomials in $n$ variables with real coefficients, and many examples are included. Proofs are presented as clearly and a

Who reads Positive Polynomials and Sums of Squares (Mathematical Surveys and Monographs)?

Author

Murray A Marshall

Publisher

American Mathematical Society

Published

2008

Language

EN

ISBN

9781219961672

Category

nonfiction

Subjects

Mathematics, Stem