Positive Polynomials
From Hilbert's 17th Problem to Real Algebra
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Author
Contributions
- Delzell, Charles N. - Contributor
Publication
2001 - Springer Berlin Heidelberg, Berlin, Heidelberg, Germany
Language
English
Word Count
67,250 words, Guess
Page Count
269 pages
Physical Format
[electronic resource] :
Identifiers
- Open LibraryOL27081925M
- ISBN-139783642074455
- ISBN-103642074456
- OCLC Control Number851377023
- OCLC Control Numberpositivepolynomi00pres
Classifications
- DDC512
- LCCQA150-272
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.
Subjects
Series Statement
- Springer Monographs in Mathematics
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