Positive Polynomials
Subtitle: From Hilbert's 17th Problem to Real Algebra
By: by Alexander Prestel, Charles N. Delzell
Contributors: Delzell, Charles N.
Series: Springer Monographs in Mathematics; Springer Monographs in Mathematics
Publisher: Springer Berlin Heidelberg
Published: 2001
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 269
ISBN-13: 9783642074455; 9783662046487
Subjects: Mathematics; Algebra
Description: Positivity is one of the most basic mathematical concepts. In many areas of mathematics (like analysis, real algebraic geometry, functional analysis, etc.) it shows up as positivity of a polynomial on a certain subset of R^n which itself is often given by polynomial inequalities. The main objective of the book is to give useful characterizations of such polynomials. It takes as starting point Hilbert's 17th Problem from 1900 and explains how E. Artin's solution of that problem eventually led to the development of real algebra towards the end of the 20th century. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed. Thus the monograph can also serve as the basis for a 2-semester course in real algebra.
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Table of contents: title: I Real Fields; title: II Semialgebraic Sets; title: III Quadratic Forms over Real Fields; title: IV Real Rings; title: V Archimedean Rings; title: VI Positive Polynomials on Semialgebraic Sets; title: VII Sums of 2mth Powers; title: VIII Bounds; title: Appendix.