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Positive Polynomials

From Hilbert’s 17th Problem to Real Algebra

  • Alexander Prestel
  • Charles N. Delzell

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Alexander Prestel, Charles N. Delzell
    Pages 1-5
  3. Alexander Prestel, Charles N. Delzell
    Pages 7-29
  4. Alexander Prestel, Charles N. Delzell
    Pages 31-51
  5. Alexander Prestel, Charles N. Delzell
    Pages 53-80
  6. Alexander Prestel, Charles N. Delzell
    Pages 81-111
  7. Alexander Prestel, Charles N. Delzell
    Pages 113-137
  8. Alexander Prestel, Charles N. Delzell
    Pages 139-159
  9. Alexander Prestel, Charles N. Delzell
    Pages 161-178
  10. Alexander Prestel, Charles N. Delzell
    Pages 179-201
  11. Back Matter
    Pages 203-269

About this book

Introduction

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.

Keywords

Algebra Positive polynomials Real Algebra Semialgebraic sets functional analysis hilbert's 17th problem valued fields

Authors and affiliations

  • Alexander Prestel
    • 1
  • Charles N. Delzell
    • 2
  1. 1.Fachbereich Mathematik und StatistikUniversität KonstanzKonstanzGermany
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04648-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07445-5
  • Online ISBN 978-3-662-04648-7
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site