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Positive Polynomials

From Hilbert’s 17th Problem to Real Algebra

Paperback Engels 2011 9783642074455
€ 60,99
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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

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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.

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€ 60,99
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        Positive Polynomials