Victoria Powers

Certificates of Positivity for Real Polynomials (eBook, PDF)

Theory, Practice, and Applications

• Format: PDF

Produktbeschreibung

Produktdetails

• Verlag: Springer International Publishing
• Erscheinungstermin: 26. November 2021
• Englisch
• ISBN-13: 9783030855475
• Artikelnr.: 63042934

Autorenporträt

Inhaltsangabe

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1. Preliminaries.- 2. Sums of Squares and Positive Polynomials. - 3. Global Certificates of Positivity.- 4. Positive Semidefinite Ternary Quartics.- 5. Positivity on Semialgebraic Sets.- 6. The Archimedean Property.- 7. Theorems of Schmudgen and Putinar.- 8. The Dimension One Case.- 9. Positivity on Polytopes.- 10. The Noncompact Case.- 11. Sums of Squares of Rational Polynomials.- 12. Positive Polynomials with Special Structure.- Real Algebra and Algebraic Geometry.- Index of Notation.- Index.

Rezensionen

"The book under review is a very nice introduction to the central topic of real algebra ... . The book is very well written with many examples demonstrating the statements of the main results. ... In the reviewer's opinion this is a very nice and concise presentation of the most important pillars of real algebra up to the present time." (Aljaz Zalar, Mathematical Reviews, June, 2023)

"This book introduces several theories with applications ... . Also, the book includes introductions to various recent developments ... . The author described the results as friendly as possible with sufficient intuitions and examples. ... This book provides a good introduction to certificates of positivity who want to learn this area as a beginner." (Jaewoo Jung, zbMATH 1483.14001, 2022)