Alexander Prestel,
Charles Delzell
Springer Berlin Heidelberg
0e druk, 2011
9783642074455
Positive Polynomials
From Hilbert’s 17th Problem to Real Algebra
Specificaties
Paperback, 269 blz.
|
Engels
Springer Berlin Heidelberg |
0e druk, 2011
ISBN13: 9783642074455
Rubricering
Onderdeel van serie
Springer Monographs in Mathematics
Levertijd ongeveer 8 werkdagen
Samenvatting
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.
Specificaties
ISBN13:9783642074455
Taal:Engels
Bindwijze:paperback
Aantal pagina's:269
Uitgever:Springer Berlin Heidelberg
Druk:0
Inhoudsopgave
1. Real Fields.- 2. Semialgebraic Sets.- 3. Quadratic Forms over Real Fields.- 4. Real Rings.- 5. Archimedean Rings.- 6. Positive Polynomials on Semialgebraic Sets.- 7. Sums of 2mth Powers.- 8. Bounds.- Appendix: Valued Fields.- A.1 Valuations.- A.2 Algebraic Extensions.- A.3 Henselian Fields.- A.4 Complete Fields.- A.5 Dependence and Composition of Valuations.- A.6 Transcendental Extensions.- A.7 Exercises.- A.8 Bibliographical Comments.- References.- Glossary of Notations.