Positive Polynomials: From Hilbert's 17th Problem to Real Algebra / Edition 1

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Overview

Positivity is one of the most basic mathematical concepts, involved in many areas of mathematics (analysis, real algebraic geometry, functional analysis, etc.). The main objective of the book is to give useful characterizations of polynomials. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed.

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Editorial Reviews

From the Publisher

From the reviews of the first edition:

"This is a nicely written introduction to ‘reality’ and ‘positivity’ in rings, and besides students and researchers it can also be interesting for anyone who would like to learn more on positivity and orderings." (Vilmos Totik, Acta Scientiarum Mathematicarum, Vol. 68, 2002)

"A book on ‘real algebra’ that serves as an introduction to the subject in addition to the main theme of the text. … Well written with exercises for every chapter." (ASLIB Book Guide, Vol. 66 (11), 2001)

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Product Details

  • ISBN-13: 9783540412151
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 5/18/2001
  • Series: Springer Monographs in Mathematics Series
  • Edition description: 2001
  • Edition number: 1
  • Pages: 269
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.69 (d)

Table of Contents

I Real Fields.- II Semialgebraic Sets.- III Quadratic Forms over Real Fields.- IV Real Rings.- V Archimedean Rings.- VI Positive Polynomials on Semialgebraic Sets.- VII Sums of 2mth Powers.- VIII Bounds.- Appendix.
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