E-Book, Englisch, 268 Seiten, eBook
Prestel / Delzell Positive Polynomials
2001
ISBN: 978-3-662-04648-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
From Hilbert’s 17th Problem to Real Algebra
E-Book, Englisch, 268 Seiten, eBook
Reihe: Springer Monographs in Mathematics
ISBN: 978-3-662-04648-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
